The 20-year old was stopped by police in Spearwood at about 1am on Sunday, the club confirmed.
It marks Carter’s second slip up in five months, having breached COVID protocols in April after a social media video surfaced showing him at a house gathering.
“Jason put the lives of other road users and himself at risk by getting behind the wheel after consuming alcohol,” Dockers CEO Simon Garlick said in a statement.
“As a club, we believe it is important to hold this type of behaviour to account.
“Therefore, the club has determined that Jason will be suspended for five games, be required to step away from the club during that time and also undertake an alcohol counselling and education program.
“Jason is a young man who has clearly made a poor decision but can learn from this experience.
“The club will continue to work with Jason and his management to ensure he is provided with the appropriate amount of guidance and support during this time.”
Carter has played two senior games for Fremantle after being drafted as a category B rookie in 2018.
Understand there is a drink driving indiscretion involving a Dockers player. It’s not a covid protocol issue. I expect the club will suspend the player. Details to follow @7NewsMelbourne
— Tom Browne (@TomBrowne7) August 18, 2020