The Saracens front-row forward was ruled out for three months with a hamstring problem in May, meaning he was playing for the first time since the injury on Sunday (AEST), a matter of weeks before the Rugby World Cup.
But Vunipola failed to finish the game after coming on as a replacement, prompting fears of a major issue ahead of the tournament in Japan.
Coach Jones was unsure of the extent of the problem but stayed optimistic after an impressive 57-15 win at Twickenham.
"He just felt his hamstring a little bit," Jones said. "We're not sure how serious it is. We're cautiously optimistic he'll be okay."
There was a moment of concern for Ireland, too, with Cian Healy hobbling off shortly before half-time after receiving treatment for an ankle problem.
There was also a head injury assessment (HIA) for Conor Murray, who briefly came back on before being withdrawn.
Ireland coach Joe Schmidt was positive, saying: "Conor passed his HIA, he was fine.
"We had a bit of a breakdown in communication - I wasn't going to put him back on, so that was a slip-up on our behalf and we got him off.
"Cian's had an x-ray and the ankle is normal. He sprained it and was pretty uncomfortable. The good news is he did walk from the pitch, so hopefully that's a little bit of promise for us."