The 31-year-old Scot, who has not played since Wimbledon last year, had a hip operation in January.
He had hoped to play in the grass-court Libema Open in s’Hertogenbosch in the Netherlands, starting on 11 June.
“I am not quite ready to return. I am still aiming to play in the coming weeks, but I want to be 100% when I do return,” said Murray.
“It is with regret that I won’t be ready to play in s’Hertogenbosch. I was excited to play there for the first time.”
Murray, the British number two, has won Wimbledon twice – in 2013 and 2016 – and this year’s tournament starts on 2 July.
The Fever-Tree Championships at Queen’s in London takes place from 18 to 24 June, and there are grass-court tournaments in the Turkish city of Antalya and Eastbourne in the week before Wimbledon.
“I’ve been out close to a year now, which is a lot longer than me or any of my team expected, but I’m getting closer to playing again,” added Murray.
“I’ve started training a few days ago and am hoping to make my comeback during the grass-court season.”
Earlier this week, his mother Judy told BBC Sport that Murray would not risk playing at Wimbledon unless he was fully fit.
“The most important thing is he gets fit again for the long term and any top athlete would tell you they would not come back until they felt they could give 100%, especially in a major like Wimbledon,” she said.