Frazier also informed Donovan McNabb that he was being demoted.
The sports agency that represents Ponder tweeted Tuesday that the rookie quarterback will start for the Vikings on Sunday against Green Bay.
"Congrats to #Vikings client @cponder7 for earning the start for next week's game," SportsTrust Advisors posted to its Twitter account.
The Associated Press left messages for agent Jimmy Sexton, and a Vikings spokesman said the team would not comment until Wednesday.
With the Vikings 1-5 and coming off of a 39-10 loss at Chicago, the move was widely expected. Frazier said Monday that he would take the next two days to evaluate the position and make an announcement on Wednesday.
Frazier hand-picked 34-year-old McNabb to come in and try to help the Vikings avoid a rebuilding year. But the veteran has struggled to find consistency in a new offensive system. He ranks 29th in the league in touchdowns, 26th in yards passing and 19th in completion percentage.
For the first five weeks of the season, Frazier steadfastly stood behind McNabb, defending him amid all the criticism from fans and the media. But Frazier backed off of that on Monday.
"The only qualifier is what's best for our team, and that will be the criteria we use when we sit down and continue these discussions over the next couple days," Frazier said.
Ponder, who was taken with the 12th overall pick out of Florida State in April, made his NFL debut in the fourth quarter against the Bears on Sunday night. Playing with a huge deficit, Ponder went 9 for 17 for 99 yards.
"For a guy who gets limited reps in practice, it seems he had a good grasp, like we thought he would, of our offense," Frazier said Monday.
The Vikings were off on Tuesday, so McNabb and Ponder were unavailable for comment.
Frazier was adamant when he took over the job on a permanent basis in January that the team was not rebuilding and expected to contend in 2011. That was the biggest reason he pushed for McNabb.
Drafting Ponder was a look to the future, but the summer-long lockout prompted the Vikings to look for a veteran quarterback to bridge the gap until Ponder was ready to take over.
Frazier had a close relationship with McNabb dating to their days together in Philadelphia, and the coach was confident McNabb had enough left in the tank to help the team avoid having to bottom out before turning the team over to Ponder.
But McNabb struggled, allowing opposing defenses to concentrate almost solely on stopping Peterson and the running game. He was booed lustily by impatient Vikings fans in a 34-10 win over Arizona two weeks ago, and it could have been even worse if McNabb took the field against the Green Bay Packers on Sunday at the Metrodome.
It certainly hasn't all been the quarterback's fault. A leaky offensive line hasn't given McNabb much time to throw, his receiver corps lacks the big-play deep threat that can loosen up a defense and new offensive coordinator Bill Musgrave has made several curious calls in all six games that have helped stall Vikings drives.
Now it will be up to Ponder to see if he can give the team a much-needed spark against the defending Super Bowl champions.
The 23-year-old showed plenty of mobility and athleticism in the preseason, which could serve him well against Clay Matthews and the Packers defense.
The other remaining question will be how McNabb, a proud veteran, handles the demotion. After the Bears game, McNabb made it clear that he expected to be the starter against the Packers. And he's coming off his best statistical game in purple, having completed 19 of 24 passes for 177 yards.
One thing is certain -- this is Ponder's job now. Frazier said Monday he wasn't interested in rotating quarterbacks in and out.
"You don't want to be (in) Week 8 or 9 and flip-flopping quarterbacks," he said. "Once a decision is made, if we were to decide to go with Christian, you'd like to be able to say that this is the way to go. You don't want to be, in my mind, going back and forth."
Information from ESPN senior NFL analyst Chris Mortensen and The Associated Press was used in this report.