French-born Mouret created a capsule collection of 10 dresses for the US clothing chain in classic styles, including tunic, shift and shirt dresses in navy-blue, red and black.
The limited-edition tunic and shirt dresses were priced between£45 and£78, with more than 150 an hour sold at Gap's flagship store on Oxford Street.
Designer Mouret is best known for his£800 galaxy dress, worn this year by a number of celebrities, including Rachel Weisz and Keira Knightly. As such, consumers consider the dresses at Gap a steal, at less than£100 each.
Half of all profits from the three red dresses will go towards the Global Fund to Fight Aids, TB and Malaria, as part of the Red project, founded by U2 lead singer Bono.
A Gap spokeswoman said: 'It has been very busy. Some stores have sold out. It has been phenomenal.'
The company is following on from the success achieved by value clothing retailer H&M, which brought haute couture to the high street. The stampede at Gap was similar to that seen for designer Stella McCartney's sell-out H&M collection.
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