The Wimbledon and Olympic champion believes the uninvited guest followed him to two tournaments after she was spotted at his hotels.
Despite having a 'do not disturb' sign on his door in the first incident, Murray said the maid let herself in and approached his bed before perching by his side and touching him.
The 29-year-old described the behaviour as "extreme", after disclosing the startling information when asked to explain what the 'craziest thing' one of his fans has done.
In an interview promoting the International Premier Tennis League, Murray said: "At one of the tournaments I played, a maid in the hotel ... I had a 'do not disturb' sign on, on the door, and she came in and sat on my bed and started stroking my arm at about seven in the morning when I was still sleeping, and then turned up at a couple more tournaments in the hotels that I was playing at in Rotterdam and Barcelona.
"I don't know if that's a fan thing - that's a bit extreme - but that happened."