Gov. Mike Huckabee of Arkansas today refused to authorize a Medicaid payment for an abortion for a 15-year-old girl whose stepfather has been charged with incest, despite a Federal judge's order that such payments were required by Federal law.

Through a spokesman, Mr. Huckabee said his first obligation was to obey the Arkansas State Constitution, rather than Federal law. The State Constitution includes an amendment banning the use of public money for abortion except when a mother's life is endangered; the Federal statute requires that Medicaid pay for abortions that are performed on poor women in cases of rape or incest or a threat to the mother's life.

Aides to Mr. Huckabee, a Southern Baptist minister, emphasized that his refusal to authorize the payment of the $430 claim did not reflect his well-known opposition to abortion but was a carefully considered strategy to protect the state's position in a pending lawsuit in a state court. In that action, an anti-abortion advocate is seeking an order compelling Arkansas's withdrawal from the Medicaid program because of the state constitutional provision. A part of the state's position has been that the case is moot because no one in Arkansas has sought Medicaid reimbursement for an abortion before.

But Carolyn Izard, the supervisor of the clinic that performed the abortion on the young patient last week, called Mr. Huckabee's position ''nonsense.''