The game, which Boro eventually won 3-2, had to be stopped by referee Chris Sarginson shortly after Scott McDonald had put the visitors 2-1 ahead when goalkeeper Jason Steele and an assistant referee were targeted with missiles thrown by the home fans.
Ambler told the club's official website: "The FA have taken into account the arrests made, and the steps that Millwall FC have, and continue to implement, to stop similar incidents occurring in the future.
"However, the FA have informed us that they will monitor every game between now and the end of the season. They have advised us that they can take retrospective disciplinary action, including the Middlesbrough match, should there be any further incidents.
"We pride ourselves in the passion of our support and on Tuesday night we saw that with a fantastic atmosphere at The Den against QPR which undoubtedly helped the team.
"That is the type of support we want to help the club continue to move forward. Incidents such as those that blighted the Middlesbrough game obviously hinder the progress we are making."