Farrell, who was a late arrival in New Zealand due to the English club final, played in the second test at Dunedin, won 28-27 by the All Blacks to clinch an unassailable 2-0 lead in the three-match series.
The England team said he would remain with the squad until the end of their tour, which concludes following the third test in Hamilton on Saturday.
"The knee has been scanned and there is a strain there," England coach Stuart Lancaster said in a statement.
"It's disappointing for Owen as he was desperate to play in the final test but such is his character that he is already working on his rehab and still contributing to the tour.
"Fortunately we have three other flyhalves to call on and well make that selection call over the next few days."
Freddie Burns played in the 20-15 first test loss at Eden Park and was impressive filling Farrell's shoes and is likely to get the nod again from Lancaster to play at Waikato Stadium.
(Reporting by Greg Stutchbury; Editing by John O'Brien)
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