Iran's military government, in a move that appeared calculated to suggest some distance between the new regime and Shah Mohammad Reza Pahlavi, yesterday set into motion investigations into the finances of the royal family and the Pahlavi Foundations.

The new prime minister, Army Gen. Gholam Reza Azhari, announced that a commission had been set up to probe the financial affairs of the monarch's family, many of whom had already left the country before the anti-shah rebellion reached its peak Sunday. It was subdued following the installation of a military government.

In recent weeks, many members of the royal family, including the shah's brothers and sisters-in-law, reportedly have fled Iran.

The government said the special commission will have two months to present the results of its investigation, which was said to delve into alleged misappropriations of funds amassed by the government during Iran's multibillion-dollar oil boom over the past decade.

The government said that another commission will be created within a month to investigate the Pahlavi Foundation which is owned by the royal court. Critics of the monarch say the foundation is a front for the shah's financial holdings. Its annual income has been estimated at $1 billion, tax-free, and has made the royal family one of the richest in the world.

A major irritant to traditional Moslem leaders in the anti-shah movement has been the foundation, which holds a quarter of Iran's agricultureal land. The remainder was subdivided 15 years ago.

Farmers who work on the Pahlavi land are paid by the foundation, a system which affronts traditional Moslem precepts that a farm's harvest should belong to the tiller.

Opponents of the shah say the royal family has gotten rich at the expense of the farmers, and have long called for an investigation of the agricultural measures adopted by the monarch. The government, in a terse announcement of the investigation, said that "all departments" of the foundation will be probed.

Opponents of the shah often have criticized the government for ignoring the royal family in previous corruption probes. One of the shah's closest relatives, his twin-sister Princess Ashraf, has been accused of involvement in a number of questionable enterprises, and there have been frequent foreign press allegations about her ties to the illicit opium trade.

Another sister of the shah, Princess Shams, moved into a $500,000 apartment in the Shoreham West in 1975. The apartment is still maintained by the royal family, although Princess Shams has since moved to the West Coast, where she owns an expensive home.

Coupled with the continuing anti-corruption drive that already has resulted in the arrest of scores of former officials, the current investigations were widely interpreted here as an attempt by the new government to placate moderate anti-shah political groups and Shlite Moslem mullahs, whose opposition to the shah's modernization program first fueled the insurrection here.

"The government in obviusly trying to establish its creditability with the people, and it is doing it in a very showy way," one Western diplomat observed.

For the second day in a row, the state-owned Iranian radio and television broadcast announcements of the arrest of former prime minister Amir Abba Hoveyda, but added no new details. Hoveyda presided over the development boom years of 1965 to 1977, and was a close political ally of the shah.

The consensus of several Iranian political figures and informed diplomatic analysts was that the next few weeks will be critical in determining whether the shah can rehabilitate his image among dissatisfied moderates, thereby isolating the Moslem leaders and radical elements of the opposition.

If the present relative civil calm holds on and the government is able to put an end to the wave of strikes that have threatened to put Iran's economicy into a state of chaos, the observers chave concluded, then the shah can weather the storm, in the short run at least.

Demonstrations announced by opposition figures in the last two days have not come off in the face of a massive show of force by army troops, but several opposition leaders are predicting a resurgence of urban geurilla activity by two underground groups comprised of Moslem youths and Communists.

Moreover, opposition sources said yesterday that they expect workers' strikes to intensify on Sunday, the day after a Moslem holdiay, which is sure to exacerbate the economic problems and tempt the government to crack down on the strikers, thereby renewing tensions.

In the next year, wage increases promised to government workers already will total $6 billion, or a third of Iran's $21 billion oil revenue. The government already has a $1.5 billion deficit this year, and is facing a $13 billion debt potential in the next year, economic analysis said.

The Central Bank of Iran recently began injecting 500 billion rials - about $700 million - into the economy, worsening inflation. Last year, inflation peaked at 31 percent, and next year economists expect inflation to be between 40 and 50 percent.

In still another conciliatory gesture, the government yesterday announced that Azhari had asked provincial governors-general to form committees made up of religious leaders and lay politicians to survey civil disturbances and begin arresting "agitators."

The inclusion of Moslem leaders on the proposed committees was seen here as an attempt to court favor with the moderate religious opposition and further isolate Shiite leader Ayatollah Ruhollah Khomeini, who is in exile in France, but still directs much of the anti-shah opposition.

In a day notable for the absence of organized protest, the government also reconvened the Majlis, or parliament, which immediately voted to suspend parliamentary immunity for a member who had been accused of corruption in connection with illegal imports.

The Majlis had been suspended indefinitely - tantamount to its dissolution - but political observers' said that the military government would now keep it active because disbanding it would, under the constitution, require elections within 90 days.

The government is said to be reluctant to commit itself to elections then, because nobody is certain of what theclimate will be like in three months, or whether civil order can be manintained that long. The shah has publicly pledged himself to holding elections when law and order are restored.