The Senate early yesterday voted 56 to 42 to give President Reagan $988 million in MX production money but not let him spend it until he can win congressional approval on how the missile will be deployed.

Last night, Reagan announced that he will appoint a special bipartisan commission of "senior officials from previous administrations as well as technical experts" to come up with an acceptable basing plan. The commission, whose likely members were not identified, would be similar to the one Reagan appointed last year to find solutions to another basic problem: how to shore up the Social Security system.

In a statement, Reagan pledged the commission's "fullest possible cooperation" with Congress in making "the most exhaustive renewed analysis possible of every apparent option." He said it is "essential that every member of Congress and indeed as many as possible of the American people gain a full appreciation of alternative solutions to this problem."

Reagan called the Senate vote on the MX "welcome and wise," although it was something of a setback for him since he originally had asked that the production funds be approved unconditionally.

But in a concession to the White House the Senate did agree to require that Congress vote on a deployment plan within 45 days after the president recommends one, which it said should be no earlier than next March 1.

The White House said it was pleased by the vote, because the production money was approved after the House had deleted it. But the House, in the conference on the issue expected to start today, is considered unlikely to agree to the requirement that Congress act on the deployment plan within a fixed time.

Thus the Senate vote, in which 15 Democrats joined 41 Republicans, was a "symbolic, more than a substantive victory" for President Reagan, said Sen. Mark O. Hatfield (R-Ore.), chairman of the Appropriations Committee. "If the White House wants to cry victory, I don't mind. But anyone can see that the president simply didn't get the money to spend for production. That's the bottom line."

The vote came on a motion by Sen. Henry M. Jackson (D-Wash.). The MX money is included in the so-called continuing resolution designed to carry otherwise unfunded government agencies, including the Pentagon, into the new year.

The main issue with MX has been to find a way to base it that would leave it relatively invulnerable to attack. Reagan was critical of President Carter in the 1980 campaign for having failed to come up with such a plan.

Reagan then came up with his plan, called Dense Pack, under which 100 missiles would be bunched close together in hardened silos in Wyoming. The theory is that incoming missiles would also have to be bunched, so that when the first exploded it would blow up the others. Critics have ridiculed this as being unworkable.

MX opponents say this month's House and Senate votes mean Dense Pack is dead. Some say the MX may be dead as well, and that the Pentagon will have to start over in its search for replacements for its existing Minuteman missiles.

Both the House and Senate would leave in this year's budget $2.5 billion in research and development money for MX, partly for work on a basing method.

Under the Jackson amendment, co-sponsored by Sens. John G. Tower (R-Tex.), John W. Warner (R-Va.), Ted Stevens (R-Alaska) and others, the president would submit no earlier than March 1 a detailed technical assessment of Dense Pack and alternative basing systems, as well as detailed technical assessments of other missiles that might replace the MX. He would have to reaffirm his selection of Dense Pack or propose an alternative.

The Jackson amendment, which allows the Senate a maximum of 50 hours of debate before it would have to approve or disapprove the basing recommendation, has the effect of barring a filibuster which, administration supporters fear, would effectively kill the funding for 1983 and perhaps indefinitely. But MX opponents could still prevent production by voting the basing plan down.

During the debate, which lasted until 3 a.m., Tower argued that Congress should not dismiss MX and Dense Pack just yet. "It's easy to make anything look ridiculous," he said, suggesting that the press had unfairly described the problem. "I don't know anyone who's won a Pulitzer Prize for saying something nice about a weapons system," he said.

However, Sen. Ernest F. Hollings (D-S.C.) said the administration "is totally unprepared to make a submission by March 1, unless they go bam-bam" without a serious reexamination of Dense Pack's technical problems. "There's no reason for a bum's rush," he added.