Tottenham Hotspur defender is being disciplined by the club.
The amount is two weeks wages for the England international.
Rose upset the Tottenham hierarchy with an explosive interview just days before the 2016/17 season kicks off.
The fine is for giving an interview without the club's permission.
Rose is reported to be ready to contest the severity of the fine.
The defender has not played since early 2017 after suffering an injury, and will not be involved when Tottenham visit Newcastle United on Sunday.
Despite this, Rose's interview will cast a shadow over the build up to the game, and is an unwanted distraction to a usually laser focused Mauricio Pochettino.
Tottenham have not made any signings this summer to date, and have sold regular right-back Kyle Walker.
It is this lack of investment and salary caps which has left Rose unconvinced of the club's direction and prompted him to speak his mind in his controversial Sun interview.