Members of the group are said to be "rallying around" to support Mick, with Keith Richards saying: "No one saw this coming. Mick’s always been my soul brother and we love him. We’re thick as thieves and we’re all feeling for the man.
"We really hate to disappoint our fans but we’ll see everyone really soon."
Rolling Stones drummer Charlie Watts has admitted that the death of L'Wren - who Mick had been involved with since 2001 - may be affecting the frontman's health.
Charlie said: "He’s not really well. He’s not really here. It was such a shock."
Mick himself spoke publicly about L'Wren's death for the first time on Tuesday, saying: "I am still struggling to understand how my lover and best friend could end her life in this tragic way. I will never forget her."