"Irish rugby will miss him and even more so world rugby," Howley said from Wales' training base in London.
Irish media reported that the muscle may have been detached from the bone when O'Connell was driven back by France lock Pascal Pape at a ruck, just before halftime in Sunday's match.
O'Connell has played on through many injuries - he even packed down for a scrum with a broken arm in the first test between the Lions and Australia in 2013 - but the warrior from Limerick couldn't get up from this.
The last sight of O'Connell in international rugby will be him waving to Ireland fans as he was being driven off at the back of a motorized stretcher at Millennium Stadium.
O'Brien will also be missing from Sunday's game against Argentina after he was handed a one-week ban for swinging his forearm into Pape's stomach in the opening 30 seconds of the France game.
He was cited on Monday and accepted the charge of foul play at a disciplinary hearing on Tuesday.
With flanker Peter O'Mahony ruled out of the World Cup on Monday with a knee injury and star flyhalf Jonny Sexton struggling with an adductor problem, Ireland has a big leadership vacuum to fill for its quarterfinal in Cardiff on Sunday.
O'Connell's absence is the biggest blow, though."The team talk does write itself ultimately this week," said Ireland flanker Chris Henry, who revealed he was reduced to tears by O'Connell's pre-game team talk against France.
"If you look at past games whenever Ireland have faltered, it's usually Paulie (O'Connell) that generates something, smashes someone, or gets the ball and does something different. He just keeps going when there's a brick wall in front of him. If we can use that as inspiration, then we will."
O'Connell finishes his international career with 115 test caps, including 108 for Ireland - third on the country's all-time list - and seven for the British and Irish Lions. He won three Six Nations titles and a Lions series in 2013.
He was in the starting XV in 99 games for Ireland and captained the team 28 times.After spending his club career to date with Munster, O'Connell has signed a two-year deal with French giant Toulon for what could be his final seasons in rugby. That spell may be truncated because of surgery.
He was replaced in Ireland's squad by Mike McCarthy.The injuries to O'Mahony and Sexton also came in the brutal match against the French, which Ireland won to top Pool D and avoid a quarterfinal against defending champion New Zealand.
Outside center Jared Payne was ruled out of the tournament on Saturday because of a foot injury.The squad enjoyed some light-hearted relief on Monday when players took to the golf practice range with Rory McIlroy, a four-time major winner who was visiting the team base.
There was plenty of laughter when Luke Fitzgerald - urged to "grip it and rip it" by his teammate - let his club slip mid-shot and it went flying 30 meters forward. The golf ball, meanwhile, toppled off the tee and came to rest a couple of inches in front.
Captured on camera, the video has become a YouTube hit, with nearly 150,000 views.
It was back to the serious stuff on Tuesday as the squad returned to light training and coach Joe Schmidt tried to figure out how to replace potentially five of his front-line players against Argentina.Jamie Heaslip will take over the captaincy, Iain Henderson is set to replace O'Connell in the second row, and Henry likely will come in for O'Mahony on the blindside flank.
Henry returned to the Ireland team only in May after having a mini-stroke ahead of the November test with South Africa last year.
