The change was announced before Sunday's game against Tampa Bay.
Nathan had blown save opportunities Thursday and Saturday in games eventually won by the Rays. The right-hander missed all of last season after having right elbow ligament replacement surgery, and has been inconsistent this year.
"Until I start getting that back, and I know I will at some time, I don't want to put this team at any risk and cost them ballgames right now," Nathan said. "I just thought it was the right thing to do for the ballclub and myself. Give myself a chance to get out there and still pitch on a consistent basis. Obviously that's what I need to do. Getting away from where every pitch could cost us a game."
Nathan is 0-1 with an 8.44 ERA in six games. He had converted all three save chances before his last two outings against Tampa Bay.
"It's one thing to go through his process of coming back from Tommy John surgery and trying to finish ballgames," Nathan said. "Hopefully this move will help me get some consistency, get comfortable. I have to be fair to this team, to the staff, to myself. I have to be honest. If I'm going out there not a 100 percent physically or mentally right now, the smartest thing to do is give it to somebody else."
Nathan went to see manager Ron Gardenhire and pitching coach Rick Anderson to discuss the closer role after Saturday night's 4-3 loss to the Rays, in which Nathan gave up two runs in one-third of an inning.
"It's not like I'm miles away," Nathan said. "I don't think this is too far off."
Capps had a combined 42 saves last year for the Twins and Washington.
"I kind of have mixed emotions," Capps said. "Obviously it's something I want to do and something I enjoy doing, but it's not the way I wanted it to happen."
Capps got his first save of the season, pitching a scoreless ninth in Sunday's 4-2 win.
Also, first baseman Justin Morneau was out of Sunday's lineup with the flu.
Catcher Joe Mauer was back at the ballpark after spending the previous two days at the team hotel because of a viral infection. The team feels the infection increased his body soreness recently. He was placed on the 15-day disabled list Thursday because of leg weakness stemming from offseason arthroscopic surgery on his left knee.
Mauer said he lost 12 pounds.
"I'm still not very good," Mauer said. "A lot better than the last couple days, though. It's been beating on me the last couple days."
Mauer hit .235 with four RBIs in nine games this season.
"It goes back to spring training," Mauer said. "I thought I built up enough strength in my legs to get to the season, and once the games started playing my hope was that I'd get stronger and stronger. It just went the other way. I need to take time off and get healthy. With one leg not strong, it affects other things."
The three-time AL batting champion and 2009 AL MVP is scheduled for a follow-up visit to a specialist in Baltimore on Monday. The doctor treated a lower-back problem that put Mauer on the DL for a month in 2009.
Mauer is expected to start a rehab program this week in Minnesota. Gardenhire hopes Mauer can return in a couple weeks.