Taylor suffered the injury early on in City's 2-1 victory over Ipswich Town and O'Driscoll has revealed that the 24-year-old could be forced to spend the rest of the season on the sidelines.
O'Driscoll told BBC Radio Bristol: "We've got a copy of the X-ray and it's a clean break.
"We're not sure if he needs a plate putting in - we'll decide that in the next couple of days. If that happens then his season's over."
Taylor has scored one goal in 23 appearances for the Robins this season.