His death was announced in a tweet by talent agency Conway van Gelder Grant.
Born in 1925, the Rada-trained actor performed with the RSC and starred in the first production of Equus in 1973 .
The National Theatre also marked his passing on Twitter, calling him "one of the most highly-regarded actors of his generation".
Other notable stage roles included the Fool alongside Paul Scofield in Peter Brook's 1962 production of Shakespeare's King Lear.
He also travelled the world with a one-man performance of St Mark's Gospel and played a detective in Alfred Hitchcock's Frenzy.
To many, though, he will be best remembered for his brief appearance as Q - here nicknamed Algy - in 1983's Never Say Never Again.
"Now you're on this, I hope we're going to have some gratuitous sex and violence!" he was seen telling Connery's James Bond in the "unofficial" remake of 1965's Thunderball.
The character Q has also been most recently played by Ben Whishaw, as well as Desmond Llewelyn and John Cleese.
McCowen, who was made an OBE in 1972 and a CBE in 1986, is survived by his sister Jean, two nephews and two nieces.
His partner, the actor Geoffrey Burridge, died in 1987.
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British actor Alec McCowen, who played gadget inventor Q opposite Sir Sean Connery in "rogue Bond" film Never Say Never Again, has died at the age of 91.