Best is seeing a specialist in Belfast today to determine the extent of the injury and the recovery period that will be required.
Meanwhile, Ulster picked up a number of injuries during their bonus point victory over Edinburgh at Ravenhill on Friday night.
Young Ireland international Iain Henderson, who missed the GUINNESS Series through injury, damaged his hamstring against Edinburgh and had to be replaced in the 18th minute. He is having an MRI scan this afternoon to determine the extent of the injury.
Henderson's second row partner for the RaboDirect PRO12 game, Lewis Stevenson, sustained medial ligament damage in his right knee and will be out for up to six weeks.
Regular number 8 Nick Williams suffered a calf injury ahead of the Edinburgh match and is facing a lay-off of four to six weeks.
Backs Michael Allen and Ian Porter were in the wars too against the Scottish side, with winger Allen going off in the 22nd minute after suffering concussion. He will follow the normal return-to-play protocols.
Scrum half Porter was unable to take his place on the replacements bench on Friday as he irritated his AC joint beforehand. He is expected to be unavailable for two weeks.
In a statement, Ulster Rugby also confirmed: "Darren Cave and Luke Marshall had cramp in the Edinburgh game but are expected to be available for selection this weekend (against Zebre).
"Johann Muller and Jared Payne have been progressing well through their rehab. A decision on their involvement will be taken later in the week."