The defender limped out of yesterday’s dismal 2-0 defeat to Southampton at the St Mary’s Stadium.
Taylor felt his hamstring late in the game, and was replaced at the back by fit-again James Perch.
Alan Pardew has captain Fabricio Coloccini back from suspension for Wednesday night’s game against Stoke City.
Alan Pardew: “We’ve got injuries, and we’ve got another one.
“Steven Taylor’s got an injury. He’s got a hamstring. I think he’ll be doubtful for a couple of weeks.
“We’re missing some key players, but one of them (Coloccini) will be back on Wednesday night, thank goodness.
“It looks like Steven’s going to miss out (against Stoke), so it’s one thing after another.”
Coloccini has now served the three-game suspension he was handed for a crude challenge on Liverpool’s Luis Suarez.
Perch has recovered from the groin problem he suffered against Liverpool earlier this month.