The teenager was walking through Peel Park in the Lower Broughton area of Salford at about 8.15am on Wednesday.
The offender – a white man in his 20s or 30 – stole her mobile phone before running towards Chapel Street.
Greater Manchester Police said the girl was unhurt but left “shaken”.
The force said it was a “deeply concerning incident” by “an unknown man clearly with sinister intentions”.
The man is described as about 6ft (1.8m) tall with short ginger/blonde light coloured hair and a short crop fringe.
He is believed to have been wearing a plain blue hooded top with a large front pocket and matching dark blue/black or black Adidas joggers with distinctive white stripes on the sides.
He was also said to be wearing running shoes which were white with some blue and red on them and a grey Puma backpack.
Anyone with any information has been asked to contact police.