Manager Mike Scioscia was still unclear on their status postgame, but said both would travel to Minnesota for the start of a six-game road trip.
"Right now, we're just trying to assess the injuries on two guys," Scioscia said. "We'll follow it up tonight, get some more information and see if we have to make any moves."
Downs, who has not given up a run in his last 11 appearances, was recently promoted to closer in place of Jordan Walden. He injured himself while ducking out of the way of a one-out J.P. Arencibia single up the middle. After being checked on by Angels trainers, the left-hander limped off the field for the second time this season -- he also hurt his right ankle at Target Field on April 12 -- with pain in the back of his knee.
"When he kind of turned to follow the ball -- the ball was hit kind of to his left -- he didn't feel a pop or anything, but got up and just felt like a strain out there," Scioscia said.
"I did sleep at a Holiday Inn, but I don't know if I'm qualified to make a medical diagnosis of exactly where he is. I can guess, but we're going to wait and let these guys figure it out."
Hawkins hurt his pinkie after catching an Omar Vizquel line drive that resulted in a game-ending double play. The 39-year-old right-hander then tweeted a picture of the finger in a splint, writing: "It's official -- fractured my pinkie on [the] last play of [the] game. Not a happy camper."
Alden Gonzalez is a reporter for MLB.com. Read his columns and his blog, Gonzo and "The Show", and follow him on Twitter @Alden_Gonzalez. This story was not subject to the approval of Major League Baseball or its clubs.