Henderson tore his hamstring on Friday against Edinburgh as Ulster casualties mounted with Dan Tuohy, Peter Nelson and Darren Cave also injured.
"Iain's type of injury has historically been up to six months [out]," said Ulster director of rugby Kiss.
"At this stage it doesn't look good in terms of the Six Nations."
Kiss added: "He has a consultation later this week and the medics will work out the best form of surgery going forward."
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Henderson's expected absence over the coming months will be a massive blow both to Ulster and Ireland.
First up, the versatile forward will miss Ulster's back-to-back European Champions Cup games against Toulouse over the next two weekends.
And following his impressive displays at the World Cup, and given Paul O'Connell's exit from the international stage, Henderson's likely absence from the Six Nations will also be a jolt for Ireland coach Joe Schmidt.
In terms of Ulster's other injuries from the Edinburgh game, Nelson (dislocated foot) is out for the rest of the season while Ireland lock Tuohy, who fractured an ankle, will be missing for at least two months.
Darren Cave's shoulder injury will keep the Ireland centre out for at least two games.
It's a grim injury toll for the Irish province resulting from the hard-fought 14-7 win over the Scots at Kingspan Stadium.
Ulster's director of rugby Les Kiss fears Iain Henderson's hamstring injury could rule the Ireland forward out for the remainder of this season.