The Magpies midfielder limped out of Thursday night's 1-1 Europa League draw with Maritimo, but club medics are confident that he did not suffer a tear.
Ben Arfa will miss Sunday's Premier League trip to Southampton and next Wednesday's visit to Stoke, but Pardew is relieved that he will not lose the influential Frenchman for a long spell.
"It's not as bad as we feared, so I think a couple of weeks, but no more than that, hopefully," he said.
Striker Papiss Cisse was also withdrawn at St James' Park, but could recover from his thigh injury in time to face Saints, while winger Jonas Gutierrez and defender James Perch are also likely to be passed fit.
Young striker Nile Ranger has been welcomed back into the squad after Pardew was impressed with the striker's change in attitude.
"Let's just say he's knuckled down," he said. "I still think he owes us and I said that to him this morning, so I'm not saying anything that I haven't said to him personally.
"I think he owes us and now is the time to be humble, come in and play football and concentrate on football."