President Reagan will veto the Orphan Drug Act, a measure designed to encourage the production of drugs for rare diseases, a White House source said yesterday.

The bill would provide tax credits of about $15 million a year through 1988 to pharmaceutical companies that develop drugs to fight diseases that afflict relatively small numbers of people. It also would grant exclusive marketing rights for unpatentable orphan drugs and clarify requirements for their approval.

Drug manufacturers say that without some kind of incentive they cannot afford to go through the rigorous procedures required for drug development.

The bill had split the Reagan administration, with top officials of the Health and Human Services Department giving it their strong support, but the Justice and Treasury departments opposing it.

Treasury officials argued that tax credits are an inefficient method of encouraging orphan drug development, and would only increase the complexity of the tax law and compound administrative problems. Justice has complained about an unrelated provision of the bill that called for a government study of the relationship between atomic testing and cancer.

The source said Reagan would kill the bill through a "pocket veto," that is, by failing to act on it within a specified time, in this case by Tuesday.

Among the diseases the bill was designed to help fight are myoclonus, afflicting 2,000 people; Lou Gehrig's disease, afflicting 9,000; and Huntington's disease, afflicting 14,000.

Congressional supporters and organizations concerned with rare diseases mounted a last-minute lobbying effort when word got out that a veto was possible. In an "open letter" to the president that is to be published in newspapers this weekend, the groups said, "Shortly before Christmas, we were shocked to learn that you are considering vetoing the Orphan Drug Act. This news turned our holidays from a time of joy to one of deep despair.

"Without the Orphan Drug Act, some of us are doomed to an early death. It is incomprehensible to us and to our families that you would reject this opportunity to alleviate so much human suffering."