The 28-year-old, who can also play in the centre, suffered the injury at the end of the Irish province's 10-9 loss at home to Northampton in the Heineken Cup on Saturday, their first defeat of the season.
"He has sustained significant lateral ligament damage to his right knee," a statement on the Ulster website said.
"He will undergo surgery later this week to repair the damage. At this stage it is not possible to put a timescale on how long his recovery period will be."
Ireland begin their Six Nations campaign in Cardiff against Wales on Feb. 2, with the first Lions tour match against the Barbarians in Hong Kong on June 1.
Bowe was an impressive performer on the last Lions tour in South Africa in 2009, starting all three tests, and has scored 26 tries for Ireland in 51 matches.
Ireland suffered more bad news over the weekend with South African-born hooker Richardt Strauss suffering a cruciate knee ligament injury as his province Leinster lost at home to French side Clermont Auvergne on Saturday, Irish media reported. (Reporting by Patrick Johnston in Singapore; Editing by Peter Rutherford)