"Unfortunately it was [a move] we felt we had to make for the team," Angels manager Brad Ausmus said. "He worked his tail off. He cared. He wanted to get back to where he was, but nothing was sticking."
Allen has a 6.26 ERA over 23 innings in 25 appearances and lost his closer role in his first season with the Angels.
"Obviously this year is not the bounce-back season I was hoping for," Allen said after Friday's appearance. "The only thing I can do is just try and get better. Either I'm going to get better or they're going to find someone else who does. That's the reality of the game."
After spending the previous seven seasons with the Cleveland Indians, Allen came to Los Angeles in free agency on a one-year, $8.5 million deal.
The 30-year-old righty had a run of five straight seasons with a sub-3.00 ERA before last year, when he had a 4.70 ERA for the Indians.
In a corresponding roster move, the Angels recalled right-hander Taylor Cole from Triple-A Salt Lake.