The announcement comes as RAF stations in Lincolnshire celebrate their 100th anniversary.
There has been some uncertainty in recent years whether the team, based at RAF Scampton, would be retained.
Sir Michael said: "They are a key part of our defence engagement..., and I don't think the public would let us lose the Red Arrows."
There has been speculation in the media in recent years that the Red Arrows could be axed as part of defence cuts in the UK.
In 2014, The Express reported the Queen was said to be worried about the team's future.
Politicians, including Labour's Vernon Coaker, have also previously said there can be no guarantees.
Speaking to BBC Look North, Sir Michael said: "Eventually we will have to replace the aircraft, and we will start to think about that in the next year or two."
He said any attempts to axe the team is "not a fight I would have".
The Red Arrows is currently taking part in a 60-day world tour aiming to promote "the best of British", which includes its first ever display in China.
RAF Waddington, Cranwell and Scampton are all holding events marking 100 years in the county.
Sir Michael added that "Lincolnshire is central to the RAF's story, and has a proud history".
He cited the Dambusters' role in World War Two, and the Vulcan involvement in the Falklands conflict, and the work being done today to tackle terrorism in the Middle East.
RAF Cranwell is also home to the RAF's Central Flying School, which under the leadership of Robert Smith-Barry, revolutionised flight training for new pilots.
Amendment: This story was changed on November 1 to reflect the defence secretary's comments that the Red Arrows fleet would be reviewed rather than imminently replaced.
The Red Arrows aerobatic team will be "around for a while yet", Defence Secretary Sir Michael Fallon has said.