Burke is leaving the company for personal reasons and it is not yet known whether she has a job to go to.
Her role will be looked after in the interim by head of brand Marsha Lenihan while the company searches for a replacement.
After a period in the chief operating officer function at Three, Burke re-joined the marketing team in her most recent role in 2010. Prior to that she had held the role of director of customer marketing.
She was part of the team that in March launched Three’s first major brand campaign in more than four years, starring a dancing Shetland Pony. Most recently Three launched its first significant push for its pay-as-you-go deals, with ads this time around featuring a pug dog called Mabel.
Before joining Three in 2004, Burke was head of customer marketing at T-Mobile, then One2One, and spent two years in a marketing role at Heinz.
Last week Vodafone and O2 switched on their 4G networks for the first time, with the former company spending significantly more on advertising to mark the switch-on. EE launched its 4G services late last year, backed by several major advertising campaigns starring Hollywood actor Kevin Bacon.
Three, meanwhile, will not switch on its 4G network until December although it will begin to raise awareness about how its customers can upgrade in its marketing before this time.