Ellis limped off after he appeared to be kicked by Ospreys lock Ian Evans during a bruising European Cup clash in Swansea last Sunday.
Evans was subsequently cited for alleged foul play, and he will appear before a disciplinary panel in Glasgow on Friday.
Ellis, who produced a sparkling try-scoring display in England's 40-3 victory over Samoa at Twickenham last month, had an MRI scan after swelling subsided on his knee.
And although he faces a spell on the sidelines, Tigers are optimistic initial fears of a lengthy lay-off have proved unfounded.
"Harry will have a small operation,' said Leicester head coach Pat Howard.
"I think he is likely to be out for a couple of weeks, and hopefully nothing too bad will show up."
England kick off their RBS 6 Nations campaign against defending champions Wales at Twickenham on February 4, when a fit Ellis would be red-hot favourite to retain his place despite competition from seasoned World Cup-winner Matt Dawson.
Leicester are facing a critical few weeks in their season. After Guinness Premiership games against Bristol and Saracens over the holiday period, they then have make-or-break European Cup appointments with French clubs Stade Francais and Clermont Auvergne.
With Ellis sidelined, Tigers will be stretched at scrum-half when they visit Bristol next Tuesday, as Austin Healey is also absent after he picked up a knock against the Ospreys.
But England prop Julian White will begin his comeback after serving an eight-week suspension.
White returns to face one of his former clubs, and it will be his first appearance since being sent off for fighting during a 16-16 draw with Newcastle on October 15.
"Obviously, it is great to have Julian White back involved," said Howard.
"He has been out for quite a while, and it will be good for him to be playing again. We are sending in two Lions props in the front-row (Graham Rowntree starts at loosehead), so that puts us in a pretty nice position."
Neil Cole is handed the number nine jersey, partnering Ross Broadfoot at fly-half, with Broadfoot starting instead of a rested Andy Goode.
Wing Tom Varndell is the only player retained from Tigers' back division on duty in Swansea, with Goode, Geordan Murphy, Leon Lloyd and Ollie Smith among those rested, while changes up front include breaks for Martin Corry, Ben Kay and George Chuter, allowing lock Louis Deacon a start as skipper.