Cleveland, which dealt second baseman Cesar Hernandez and outfielder Eddie Rosario in separate trades, also sent catcher Yainer Diaz to Houston for the speedy Straw, who will fill an open outfield spot for the remainder of this season -- and maybe beyond.
Maton, 28, has been used in a setup role this season, his third with the Indians. The right-hander was 2-0 with a 4.57 ERA in 38 appearances.
Straw, 26, batted .262 with two homers and 34 RBI in 98 games for the Astros. He has also scored 44 runs and is currently tied second in the AL with 17 steals in 22 attempts.
Straw has also played well defensively, and did not commit an error over 96 games in center field.
A right-handed hitter, Straw was drafted in the 12th round by Houston in 2015.