The local authority, who own the club's Broadwood Stadium, have issued the decree following the club's controversial decision to re-sign the striker from Raith Rovers on loan.
Goodwillie was ruled to have committed rape by a civil court judge in 2017 and his signing by Rovers, from Clyde, earlier this year led to fierce backlash.
The club said he would not play and he headed back to the Scottish League One side on loan earlier this week, but that has also been met with an outcry.
A council statement read: "We have informed the club that David Goodwillie must not be permitted access to the stadium, for any purpose, with immediate effect.
"Should Mr Goodwillie enter the stadium, we will consider the contract to have been breached and we will take immediate steps to terminate it."
"In addition, we have informed Clyde FC that the council intends not to renew the lease with the club when the contract for the use of Broadwood Stadium expires in May, 2023.
"The council utterly condemns all and any violence towards, or abuse of, women. We offer a range of services to support women who experience abuse, through Rape Crisis Lanarkshire and Aura, and we would urge anyone in this position to make contact.
"The council believes in rehabilitation, and has services which provide this. However, Mr Goodwillie has not expressed any contrition in relation to the rape which the court found he had committed in the civil action against him.
"In re-signing Mr Goodwillie, Clyde FC has not acknowledged that background or community concerns, instead choosing to focus on enabling Mr Goodwillie to play football."
The decision to bring back the striker has been met with major uproar, with the Clyde Ladies team announcing they 'no longer wish to play' for the club.
"We can today confirm the general manager/secretary of Clyde Ladies has resigned on hearing the news of the return of David Goodwillie to the club," their statement read.
"All of the players in the ladies team have discussed the situation with the general manager/secretary and they are all in agreement that we no longer wish to play for Clyde FC.
"This will start with immediate effect.
"As a group of female footballers all we wish to do is play the sport that we love but due to the current circumstances we are unable to do this.
"At this time, we wish to ensure the wellbeing and privacy of our players therefore we would ask that players are not approached personally for comment regarding this matter."