The former England under-17 international was hurt in a collision with Saints' striker Michael Obafemi and was replaced by Otto Huuhtanen after 30 minutes following a lengthy stoppage.
He was taken to hospital as a precaution but was able to report to the club's Little Benton Academy for treatment on Tuesday.
And it is hoped that, despite some bruising, the 19-year-old will be able to return to action next month.
Woolston is currently on loan with Evo-Stik North promotion hopefuls South Shields, but is able to play for Newcastle's under-23s under the terms of the agreement.