England selectors announced on Wednesday night that Flintoff would again take the reins, having led the side during its 5-0 loss to the Australians in the Ashes.
Much has been made of his workload, and Flintoff has looked a better player since Vaughan took over, culminating in his man-of-the-match performance in the drought-breaking win against New Zealand on Tuesday.
However, Flintoff was preferred over opening batsman Andrew Strauss to replace Vaughan.
Vaughan suffered the tear during England's win on Tuesday, in only his second game back after knee surgery that sidelined him for more than a year.
His injury, which eventually left him needing a runner during the triangular one-day series match in Hobart, was assessed as a grade-one or slight tear to his left hamstring here Wednesday.
He will miss Friday's clash against Australia in Brisbane and is in doubt for the following two matches in Adelaide, against New Zealand on January 23, and Australia three days later.
Lancashire batsman Mal Loye has been called into the England squad, although Vaughan is travelling to Brisbane with them.
Australian batsman Mike Hussey said Flintoff looked to be finding his best form since being relieved of the captaincy.
"He had quite a long break coming into the Ashes series, so I'm sure now he's starting to find some rhythm with his batting," Hussey said in Brisbane.
"I think now he's had a fair bit of cricket behind him (so) you'll see the best cricket he can play over the next week or two."
Hussey said Vaughan's setback was a big blow to England's tri-series hopes.
"He is a class batsman, he's performed well in Australia and he's got confidence after playing well in our country," he said.
Vaughan's injury occurred in the field against the Kiwis and although he still opened the England innings, he eventually had to call on Jamie Dalrymple to act as a runner, before being caught for 17.
His setback is on top of the cracked rib sustained by star batsman Kevin Pietersen, who has returned to England but flagged the possibility that he may return if his side reaches the triangular series finals.
Meanwhile, New Zealand is still waiting for a definitive diagnosis of fast bowler Shane Bond's latest back problem.
Bond has battled back injuries throughout his career and was forced from the field by back soreness during his side's loss to England.
New Zealand coach John Bracewell said Bond was still feeling stiff and would see a sports physician on Thursday morning, with a clearer picture of his injury status likely to emerge within 48 hours.