Nelsen had to be replaced just before half-time and manager Sam Allardyce later expressed concern that he could be out for some time.
Scans have revealed that he has torn a muscle behind the knee and suffered extensive bone bruising.
The 32-year-old will not be able to return for four to six weeks but should be fit to captain New Zealand at this summer's World Cup.
"It's probably the best result I could have got," Nelsen told Radio Sport.
"In the great scheme of things it's not too bad. It certainly could have been worse."
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