The D.C. Wage-Hour Board yesterday voted 2 to 1 to increase the minimum wage for 45,000 hotel, restaurant and apartment workers from $3.35 an hour, the current federal minimum wage, to $3.80 an hour, effective Jan. 2.

At the same time, the board exempted from its action employes under 18 years of age and certain workers at local colleges. Waiters who derive part of their income from tips were also excluded from receiving the full benefit of the increase.

The board's action came over the objections of major fast-food chains and Washington hotel managers, who fear that the mandatory pay increase will make it more difficult for them to compete with suburban Virginia and Maryland companies that only pay the federal minimum wage.

Paul A. London, an economic consultant for five fast-food chains, said yesterday that imposition of a higher minimum wage in Washington would force the local restaurant industry to eliminate 700 jobs. He also said that fast food chains will be forced to raise their prices to offset the impact of the increased minimum wage.

Board members Paula L. Jewell, the chairman, and David W. Wilmot voted for the increase. It was opposed by Joseph A. Beavers, an official of Local 25 of the Hotel and Restaurant Employees Union (AFL-CIO), who favored a larger increase.