Purves has Tweeted that she is being fired next month after just three years in the job
Purves has been in post since 2010, when she replaced longstanding Times critic Benedict Nightingale following his retirement.
Her contract will reportedly end on 11 October 2013, though it is not known whether she will continue in her capacity as a columnist for the paper.
She revealed the news in a Twitter exchange with fellow critic Mark Shenton (see below), who described it as a "shock".
Purves – who also presents Midweek on BBC Radio 4 – is the latest of a number of critics and arts journalists to be cut from newspapers recently.
Last month the Independent on Sunday fired its theatre critic Kate Bassett as part of an 'overhaul' of the paper's arts coverage.
In a message sent to theatre PRs, Purves said: "The acting editor of The Times Mr Witherow has decreed that he does not want me to continue as Chief Theatre Critic. This is not my decision in any way. At all. I am not sure who is the replacement. I carry on reviewing and maintaining the lists until 11 October. If at some future date I get a chance of some other reviewing outlet I shall take it."
Nobody from The Times was available for comment.
“@ShentonStage: “Shock news just in that another leading London theatre critic has been axed” Don’t be shy Mark. Yep, its me…
— Libby Purves (@lib_thinks) September 16, 2013
Thanks, kind theatre-tweeple. No, not a joke. No, no idea why. Ends Oct 11.Shall not vanish from back row opining, watch this space…
— Libby Purves (@lib_thinks) September 16, 2013