The decision, which was made during a meeting between club chairman Peter Winkelman and Neilson on Saturday evening, came after a 2-1 defeat away at Northampton Town.
Neilson was appointed as Karl Robinson's successor in December 2016, guiding the Dons to a 12th-placed finish in 2016-17.
However, the club currently sit in the relegation zone due to a run of one win in 11 league games, including Saturday's defeat at Sixfields Stadium.
"Robbie, Stevie and Neil have all been totally dedicated to MK Dons, working tirelessly throughout their 13 months at Stadium MK," the club said in a statement.
"We thank them and everyone at the Football Club wishes them every success in the future."
The club are yet to name an interim manager in place of Neilson, who joined from Scottish Premiership club Hearts.