Savea, 32, was forced off nine minutes before halftime in a major blow to the All Blacks, who went 2-1 down in the four-test series after a bruising loss at Soccer City.
Savea had scored two tries before his injury and his absence allowed South Africa to gain a dominance that saw them go on to victory.
“He won't travel now (to the United States). We'll work out what it will look like in the next few hours,” coach Dave Rennie told the post-match press conference.
The fourth test is in Baltimore next Saturday.
Centre Quinn Tupaea suffered a knee injury and will also be a doubt for the clash, Rennie added.
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“I'm not sure of the severity and whether that'll affect them going to America or not.”
Both teams were due to leave for the U.S early on Sunday, sharing a charter flight.
The fourth test offers the All Blacks a chance to level the series, which they led after the first clash against the Springboks a fortnight ago before suffering successive losses.
“They are world champions for a reason. Very good up front and they play a bit of footy tonight,” said Rennie.
“We probably made a few errors that allowed them supply and I thought they were a lot stronger than they had been in the first two tests. But it’s not like there is a gap between the two teams, it's very close. I don't think it's a hell of a lot in it.”