Speculation had emerged over the last couple of days suggesting Tavernier could be looking at six weeks on the sidelines, but Gerrard has confirmed such talk is way off the mark.
However, he has confirmed the right-back faces two weeks out after being rushed to hospital for an operation on his appendix.
The Englishman - who has sat out just two of Gers’ 37 games so far - will be missing as the Ibrox men kick-off their Scottish Cup campaign at home to Stranraer on Friday night.
And he is likely to be absent for both next week's Premiership showdowns with St Mirren and Hearts.
But the captain will be back in time to lead out his team during Rangers' gruelling February schedule - which involves seven games on the domestic and European fronts - after medic Mark Waller spotted the danger signs after Tavernier reported stomach pains earlier this week.
"Thankfully we've got one of the best docs in the business who sent him to a specialist straight away and we got to the problem pretty early," Gerrard said.
"He will probably be out for a couple of weeks all being well. He's had a minor procedure around his appendix that we sorted out yesterday. But it went really well."
Gerrard has seen his casualty list grow in the last few days, however.
Greg Stewart is also a doubt for the Ibrox cup tie with Stevie Farrell's League One minnows with a calf knock, while Filip Helander still faces another month out of action with his foot injury.
Top scorer Alfredo Morelos is banned for the game, while Glenn Middleton has picked up a foot injury in a reserve clash earlier this week.