The move, announced Friday, is retroactive to Thursday.
Rookie right-hander Carlos Martinez was recalled from Triple-A Memphis and will be used in relief.
The Cardinals do not believe the injury is season-ending and Westbrook said the biggest reason to place him on the DL is "to kind of knock it out, get me back to where I don't have any of those nagging things, get back to full strength."
Westbrook said he's had minor back issues in the past and what team doctors told him was "not alarming."
"When you're sore, it's hard to compete at this level," Matheny said of Westbrook. "Tyler's had a strong season and I just like where he is right now, what he brings to our club."
In his past five starts, Westbrook has given up 30 earned runs in 26 innings and said the back injury made it difficult to finish pitches.
He was on the disabled list earlier this year with an elbow injury but said the elbow has felt "pretty good" lately.
"It's really just more kind of aggravating," said the 35-year-old Westbrook, who is 7-8 with a 4.49 ERA. "It's one of the things that I've been just kind of fighting through.
"Just part of being old, I guess."
Westbrook said it's been a "grind" the past few seasons.
"It seems to be always something, but I try to battle through it and no excuses for me," Westbrook said. "I never make any and I never will."
Lyons won his first two career starts and is 2-4 with a 5.09 ERA in eight games, all but one of them starts. He's 7-2 with a 3.39 ERA in 16 starts at Memphis.
The 21-year-old Martinez made his first career major league start on Aug. 8 against the Dodgers and is 0-1 in 11 games with St. Louis. He is 5-3 with a 2.66 ERA in 12 starts at Memphis and Matheny said he could be used in long relief.