Rivera left Saturday's game in Oakland with tightness in his hamstring, and then didn't play on Sunday.
Given the soggy, rainy conditions in Kansas City on Monday, it wasn't a big surprise that Scioscia would have held Rivera out again.
"It's a little bit tight, so when he can get out there and he can run, we'll wean him back in as a DH," Scioscia said. "When that's going to be -- I don't know, but I'm hoping it's day-to-day."
Rivera missed the two games before the All-Star break with tightness in his left quad and right hamstring. He returned against Oakland on Thursday, but left the game Saturday in the third inning.
"He's feeling a little better, but it's not quite ready," Scioscia said. "It might be a couple days."
Still, a couple days is different than a couple weeks, Scioscia said. The Angels could use a healthy Rivera sooner, rather than later.
Scioscia said injured outfielders Vladimir Guerrero and Torii Hunter are progressing, but they are still weeks from returning.
Guerrero, who went on the disabled list on July 10 with a strained muscle behind his left knee and a lower hamstring strain, played catch on Monday. That's one step, Scioscia said. Guerrero is also riding a bike, lifting weights and working on his conditioning.
Guerrero and Hunter's DL stints were set retroactive to July 8, so Wednesday will mark two full weeks on the DL.
"After three weeks, we'll evaluate and see where they are," Scioscia said. "There's definite progress. How much longer? There's still some hurdles at the end to get over."
Hunter, who has an adductor strain on his right side, went through some light conditioning on the field on Monday.
"It's a long way from walking to playing in a game," Scioscia said. "But at least he's doing that."
Rustin Dodd is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.