District judge Andrew Sweet handed the 31-year-old rapper the ban after he had pleaded guilty via a letter to driving while using the device in west Kensington on March 7 last year.
The judge, sitting at Wimbledon Magistrates' Court, also fined him £2,010 ($2,498) after six more points had been added to his licence.
Before Thursday's hearing, Stormzy -- whose name is Michael Ebenazer Owuo Junior -- had six points on his licence for a previous speeding offence.
In the UK, drivers can be disqualified if they build up 12 or more penalty points within a period of three years.
Sweet said that Owuo's driving record was "not good" and criticised his "dangerous and irresponsible" actions.
The rapper's lawyer, Peter Csemiczky, said his client accepted responsibility and apologised.
Stormzy is a cult figure in the British grime scene, which blends Jamaican dancehall and hip hop for a pulsating, hard-edged sound that first electrified London more than two decades ago.
His biggest hits now appear in TV ads and in 2019 he made history by becoming the first black UK solo artist to headline the Glastonbury music festival.
