Martin, 32, is a career reliever who has played seven seasons in the Minors. He has a 4.40 ERA in 29 appearances for Syracuse this year. His 14 saves rank second in the International League.
Martin pitched to a 6.57 ERA in 13 appearances over two stints with the Nationals last season, when he made his MLB debut.
Strasburg is 10-0 with a 2.90 ERA in 14 starts this season, and he is in the midst of a franchise record 13-game winning streak.
Joe Trezza is a reporter for MLB.com based in New York. Follow him on Twitter at @joetrezz. This story was not subject to the approval of Major League Baseball or its clubs.