"We want dockless bikes to work in the area but it needs to be operationally sound," Mr Wakefield told AAP on Monday.
"Bike operators need to ensure their product is maintained and presentable for the community to use."
After issuing the warning to oBike, Reddy Go, ofo and Mobike last week, Mr Wakefield commended one of the companies for cleaning up some of their wayward bikes in the area.
Operators will be notified once the bikes have been taken to council's depot and will need to pay $70 per bike if they wish to recover them.
If they don't recover the bikes, they will be recycled, Mr Wakefield says.
Head of oBike Australia CP Lim said while they welcomed action by the authorities, the move to penalise operators instead of educating users "would only serve to stifle the start-up culture".
"We believe that Australians are learning to appreciate the benefits of a dockless bicycle sharing systems, and we will work with the relevant authorities to ensure that this alternative mode of transportation can be enjoyed by as many people as possible," Mr Lim said.
ofo says it ensures a trained operations crew is always conducting regular checks on ground for "indiscriminately parked bikes or broken bikes".
"ofo is working closely with various city councils to ensure that our bike sharing services are enjoyed and benefitting our users," a spokeswoman told AAP on Monday.
A Reddy Go spokeswoman told AAP the company no longer operated in the Waverley Council area.
Mobike has been contacted for comment.