Prime Minister John Vorster injected himself into the bitter campaign to elect his successor yesterday by announcing that a government investigation into the now disbanded Department of Information headed by one of the candidates, Mulder, has not yet been completed.

Mulder, 52, is a keen aspirant to the premier ship, which Vorster is giving up for health reasons. Vorster's statement implies that Mulder, now minister for black affairs, is not yet cleared unequivocally of wrong doing or, at least of mismanagement in administering a secret fund in the information Department.

Up to now, Mulder and Defense Minister Pieter W. Botha, 62, both hard-line conservatives, appeared to have almost equal support among the 175 caucus members of the National Party who will elect the successor in Cape Town Thursday. But Vorster's statement may considerably reduce Mulder's strength, as it will undoubtedly be seen as an indication that Mulder does not have the departing premier's endorsement.

Newspaper disclosurers of the existence of the secret fund, and of the apparent frivolous uses to which some of it was put, forced resignation of three Information Department officials and the transfer of the department from the control of Mulder, a few months ago.

The scandal reportedly caused Vorster much concern and soured him on having Mulder as a successor. It is believed by some political observers that Vorster personally favors the third candidate, Foreign Minister Pik Botha, 46, who is regarded as a moderate in the party.

In the interests of party unity, however, it is believed that Vorster would like to see the elder Botha chosen. With drift toward a hard-line stance on racial policies and international issues, Pik Botha may not be able to keep the party together, it is thought because of his lack political experience.

The party caucus is also expected to elect Vorster to the post of state president. While his fragile health will limit his political activity, Vorster's personal status will certainly enhance what has up to now been a largely ceremonial job. He probably will remain a sort of eminence grise in the party to foster its unity.

Although the party is unanimously agreed on the racially based policy of separate development, or apartheid, which prohibits the sharing of political power between the country's 4.6 million whites and its 18 million blacks there is a considerable difference of views on how fast the government should remove other forms of racial discrimination.

Vorster successfully minimized these differences because of his immense popularity among the Afrikaners, the whites of Dutch descent who dominate the National Party and the government, but his successors may not be so successful.

According to some reports, Vorster has wanted to step down since last year but was persuaded to stay on. He was forced to resign after reportedly suffering a mild heart attack in August and has been ordered to stop smoking and get more exercise.

Whoever succeeds Vorster will take over as South Africa faces its sharpest international crisis since the National Party came to power 30 years ago. It results from the decision last week to back out of a plan for U.N.-supervised elections in Nambia (Southwest Africa), which South Africa administers despite protests by the United Nations.

Last week, Vorster said South Africa would sponsor its own elections in the territory. The move is seen as an attempt to prevent the militant black nationalist movement the South West African People's Organization (SWAPO), from gaining power.

The decision further isolated South Africa from its traditional Western allies who devised the election plan. It economic sanctions now being demanded by black-ruled African states at the United Nations. In addition, the Soviet-armed SWAPO is expected to escalate its guerrilla war against the South African soldiers in Nambia, thus leading Pietoria into a long-term military commitment and a Vietnam-style conflict.