The recurring injury also forced Williamson to miss the second Test against India in Mumbai, where New Zealand went down by a record 372 runs on Monday to lose the series 1-0.
"Kane's going along okay," Stead told reporters from Mumbai on the eve of the squad's return home. "I said right from the start, I expected it to be a sustained period of time.
"Last time ... was about eight or nine weeks. I expect it's somewhere in that timeframe again."
Stead said surgery on the joint was unlikely, but he was also reluctant to predict that Williamson would be fit to face South Africa in two Tests in February and March.
"We're trying not to put a timeframe on it," Stead added. "It's all about the load on the elbow and when you're in the test arena, the extra time in training and batting as well is what tipped him over the edge, I guess.
"Kane's doing it tough, don't get me wrong. He hates the thought of missing any cricket, let alone test cricket for New Zealand."
The India series was the first in the Black Caps' defence of the World Test Championship title that they won this year.
While clearly unhappy that the side were bowled out for 62 in their first innings in Mumbai, Stead was pleased that the drawn first test in Kanpur would earn them some championship points.
"A lot of teams come here and struggle, so to pick up any points from here ... was a really good achievement," he said.
"India were just better than us in their conditions."