O'Connell suffered the injury in the 55th minute of his side's win over Ulster on Saturday and has since had a scan to determine the extent of the setback.
The 32-year-old will miss Munster's RaboDirect PRO12 play-off at the Ospreys this week, as well as the Grand Final should Munster return from the Liberty Stadium with a win.
Ireland travel to New Zealand for a three-Test series against the All Blacks, with the first international kicking off in just under a month's time.
Declan Kidney's men take on the World Champions on June 9, 16 and 23 in Auckland, Christchurch and Waikato respectively.
A four-week absence would mean O'Connell would be fit to play just days before the first Test, while a six-week lay-off would rule him out of all bar the final international.
Fellow 2009 Lion Luke Fitzgerald has already sidelined for Ireland as he requires surgery on a neck problem.
Fitzgerald, who featured in the Lions' 28-25 second-Test defeat to the Springboks three years ago, has been beset with injuries since his return from South Africa.
The Leinster wing missed the 2010 RBS 6 Nations campaign after picking up a serious knee injury against Australia in November 2009 and was subsequently overlooked for the 2011 World Cup squad.
He again missed the latest 6 Nations tournament with injury but had looked to near to regaining his best form as Leinster surged to this year's Heineken Cup Final.