Mariek Daniluk, 41, was arrested outside the Comedy Theatre in the West End where the 24-year-old is appearing in 'The Misanthrope', Daily Mail online reported.
Police waited at the stage door after Keira called them.
"Keira felt threatened by this guy who turned up a number of times and tried to speak to her," a source at the theatre said.
"He did not make any specific threats to her but she was concerned enough to call in the police," the source added.
Keira, who starred in 'Pirates Of The Caribbean', swapped the UK for the US two years ago after discovering she had five stalkers.
"I've no way of knowing if they could be potential rapists. I'm frightened out of my wits every time I see one of them," Keira had said.
Daniluk, an Eastern European living in Palmers Green, North London, was held at a police station on Thursday night.
He is due to appear at City of Westminster magistrates.
"A 41-year-old man was arrested on suspicion of harassment on Thursday. The arrest follows concern expressed by a woman," a police spokesman said.
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