The 27-year-old turned his ankle during yesterday's 32-26 victory over Samoa in his side's opening game of the series.
It was initially feared that Smith would play no further part, but he has confirmed that he is already ready to return to the field.
"I've rolled my ankle, it's swollen up a bit and they've put the boot on as a precaution," The Guardian quotes the Wigan Warriors player as saying.
"It's just swelling. We've got to get the swelling down over the next couple of days and then it's back into training.
"I'll be back on the field on Monday. We've got a big week. We need to fix a few things."
England are back in action next Sunday when they take on Australia.