The decision has been made mutually after Burnley's relegation was confirmed last week.
Parker led Burnley to the Premier League last season, but has now left Turf Moor.
"Following confirmation of the Club's relegation from the Premier League last week, Parker and the Board held discussions and mutually agreed that his time at Turf Moor would conclude," the club said.
"During his tenure at Turf Moor, Parker guided the Clarets to a record-breaking season in the 2024/25 campaign, securing Burnley promotion from the Championship to the Premier League, with a 31-match unbeaten run, keeping a remarkable 30 clean sheets.
"The Club would like to place on record its sincere thanks to Scott for his professionalism, dedication and contribution. He leaves with the respect and gratitude of everyone connected with Burnley Football Club.
"Mike Jackson, supported by the existing backroom staff, will take interim charge for the Clarets' remaining four Premier League fixtures, beginning with Friday's match away to Leeds United.
"The process of appointing a new permanent Head Coach ahead of the 2026/27 season has begun."