The 25-year-old was arrested in Ealing at approximately 5pm on Saturday and is in custody in west London.
The arrest is in relation to an ongoing investigation into the disappearance of 14-year-old Alice Gross.
Police say that despite the arrest, the investigation still remains that of a missing person.
Alice was last seen on Thursday August 28 by her family and she was reported missing after she failed to return home that evening.
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The teenager is 5ft 2in with should length brown hair and of slim build. She was reportedly last seen wearing dark blue jeans, a dark green cardigan and blue Vans shoes.
Celebrities such as talk show hosts Graham Norton and Jonathan Ross have been helping Alice’s family search for her, using the hashtag #FindAlice to help publicise the search.
Posters have also been put up around central London in an attempt to find the missing teenager.
Anyone with information should call police on 020 8358 0100; Ealing Missing Persons Unit on 020 8246 1018 or the charity Missing People on 116000.