The governor's office said she left New Mexico on Tuesday and will return Friday.
Martinez, the nation's only Latina governor, also was part of a U.S. delegation that traveled to Rome in 2013 to greet the then-new pope and attend his inauguration.
While in Washington, Martinez also plans to meet with U.S. Sen. Tom Udall, a New Mexico Democrat who on Tuesday announced new legislation to compensate communities in the wake of the Gold King mine spill.
On Wednesday, Martinez will travel to Indianapolis for meetings related to the Republican Governors Association. She currently serves as the group's vice chair.