"Shakeel Massey, 20, from north-west London, has been charged with criminal damage", a Metropolitan Police spokesman was quoted as saying.
The suspect has been remanded in custody until 30 January when he will be brought before Inner London Crown Court. No motive for the crime was given.
The incident happened on 28 December and the charges were pressed on 30 December but the media have only just been notified. The ITV news channel said the $26 million painting was allegedly ripped.
The masterpiece was created in Paris in the final days of the German occupation in May 1944 and portrays photographer and poet Dora Maar, with whom Picasso had a complicated relationship.
The art gallery has taken the painting off the display and is reportedly assessing the extent of the damage. The work is from a private collection and has been on a long-term loan since 2011.