Street, who has converted all but one of his 34 save opportunities, said he expects rest, treatment and anti-inflammatory medicine will lead to healing, but he has no idea how long that will take. He hopes it's a matter of days.
"You just hope that you get on some heavy 'anti-inflams' and you sit back," said Street, who said he has never had biceps tendinitis during a season.
Before throwing a perfect ninth inning in Tuesday night's 8-3 victory, Street had been off for seven days. There were no save opportunities during that stretch, which included a season-worst five-game losing streak.
Street felt some discomfort Tuesday and reported to the Rockies' training staff that he didn't feel much better Wednesday, and he had problems while playing catch before the game.
But Street still planned to pitch, even when he warmed up for the ninth inning.
Street has a history of pushing through injury, sometimes to his detriment. Trying to grind through a hip flexor injury last season with the Athletics led to a slump that cost him the closer job. So on Wednesday, bullpen coach Jim Wright reported to Tracy that Street didn't look right, and there was no debate.
"I don't think it's anything serious, but the message that I heard from Jimmy Wright down in the bullpen sounded to me like there was a different direction that we needed to go in," Tracy said.
Street said: "If it was left up to me I'd have jogged out there, to be completely honest. Sometimes you have to have it taken out of your hands. They made the right call.
"It's not a selfish desire, but a competitive desire to go out there and get it done. But, like Tracy said, it's not Sept. 20."
Morales, 23, made the starting rotation out of Spring Training but shifted to the bullpen after he suffered a shoulder injury and the rest of the rotation pitched so well that there wasn't a spot for him. All he has done is hold opponents to a .175 batting average (14-for-80) as a reliever.
Morales shut down the Mets on 12 pitches, and finished by coming from a 3-0 count to strike out Nick Evans. Righty Rafael Betancourt and lefty Randy Flores warmed up in the bullpen, but they were not needed.
"It's incredible, from where Franklin Morales was at the beginning of the year to where he is right now," Tracy said. "That's a pretty special bullpen guy."