Izturis, 32, appeared in 57 games with Milwaukee this season, batting .235 with two home runs and 11 RBIs.
A former Gold Glove award winner, Izturis will fill the roster spot of utility man Mark DeRosa, who was placed on the 15-day disabled list due to a left abdominal strain.
The first-place Nationals already are without All-Star shortstop Ian Desmond, who is sidelined with an oblique injury, and have used second baseman Danny Espinosa as his primary replacement. Infielder Steve Lombardozzi has filled in as Washington's starting second baseman.
The Brewers replaced Izturis with top prospect Jean Segura, who has been recalled from Double-A Huntsville.