Tuesday night's Coupe de France semi-final between Troyes and Bordeaux has been postponed due to the risk of flooding.
Torrential rain is forecast in Troyes and there are fears it will threaten the Stade de l'Aube, prompting the match to be called off for safety reasons.
No new date has been arranged, although it is hoped the fixture will take place next week.
The other semi-final between Evian and Lorient will take place on Wednesday.
The Lions board said it had "reluctantly" accepted Jackett's resignation.
Jackett said: "After almost six seasons I personally feel the time is right for a new challenge, and also for a new manager to come into Millwall with fresh ideas, to take the club forward towards its long-term goal of reaching the Premier League.
"I would like to thank the Chairman, the Board of Directors, players, members of staff and supporters of Millwall for their considerable backing.
"I have thoroughly enjoyed my time at Millwall. My family and I will always have a strong link and affinity with the club."
Lions chairman John Berylson added: "On behalf of the Board of Millwall Football Club, I want to express my thanks to Kenny for his fantastic service and achievements over the past five and a half years.
"He has played a major role in creating a stable environment at Millwall which hadn't been the case prior to his arrival.
"On a personal level, whilst respecting Kenny's decision, I wish I could have persuaded him to change his mind. He was my first acquisition as chairman of the club and has proved himself to be one of the best. I am losing a great manager, but he will remain a good friend and hopefully, golf partner.
"I know everyone associated with Millwall, management, staff, players and fans, will wish Kenny all the very best with his future endeavours, except for those times when he might oppose us on the pitch.
"We are now determined to move the club forward and build on the foundations Kenny has provided towards even greater success."
