The call was made at a scrutiny meeting of the council to discuss the problems surrounding the new vessel.
Council leader Dave Stewart said the crossing at Cowes would be free until 2 July "in recognition of the problems" and to allow feedback.
Mr Stewart said the council had ordered a review of the project by auditors.
He said it had been a "frustrating and disappointing start" to the ferry.
Since launching late on 14 May the chain ferry has broken down, run aground and been suspended by the Maritime and Coastguard Agency due to "training issues".
Cars have also been damaged getting on and off.
Shopkeeper Angie Booth, who owns Valu-4-U in East Cowes, said: "Whether I come out of this and survive I am not sure - other businesses too. We are bearing the brunt of the loss of almost six months of trade.
"Will you compensate local businesses, the same as for damaged cars?"
Transport councillor Ian Ward said compensation was up for discussion.
He added: "I don't think it's a disaster. It's a prototype. There are bound to be teething problems. There were electrical problems which the company has rectified."
He said the council authorised the manufacture of ramp extensions to resolve the problem of vehicles scraping the concrete.
He said groundings were an issue with seamanship, which had been resolved.
Shopkeepers near the Isle of Wight's troubled new "floating bridge" have asked councillors to consider compensating them for loss of business.