Mayor Marion Barry announced yesterday that the District of Columbia has belatedly qualified for a federal program that gives food to low-income pregnant and nursing women, infants, and children up to 5 years old.

The Special Supplemental Food Program for Women, Infants and Children, in operation for years in all 50 states but not in the District, will provide $1.9 million in specified foods -- such as milk, eggs, cheese and infant formula, officials said.

Barry said at a press conference that the program, to begin in April 1981, eventually will reach about 8,000 people. The maximum benefit per person will be about $35 a month, officials said.

The mayor said the program "represents my administration's ongoing commitment to lower infant mortality in the District of Columbia." Infant mortality in the District was the highest of any city in the country in 1977, and last year was still 50 percent higher than the national average.

Dr. Roselyn Epps, D.C. acting commissioner of public health, said the supplemental food program should decrease the mortality rate by giving expectant mothers enough nutrition to avoid having smaller-than-normal babies. However, Barry's own "Blue-ribbon Task Force" on infant mortality concluded earlier this year that there was not enough information available to determine whether malnutrition during pregnancy contributed significantly to the mortality rate.

Peter Santos, director of the food program for the U.S. Department of Agriculture, said past requests by the District to qualify for the program had been denied because the city failed to provide an adequate plan for administering the grant.