Fabian returned to first-team training a fortnight ago after recovering from surgery on a chronic back problem and featured in Eintracht's recent friendly against Bundesliga 2 outfit Erzgebirge Aue, but has not played competitively since representing Mexico at the FIFA 2017 Confederations Cup in June.
"Marco sees health and fitness as the same thing," Kovac said on Friday. "He thinks that if he is 100 per cent healthy, he is 100 per cent fit. Unfortunately, I don't see it like that. He's not quite there, but we'll give him time.
"We'll try to get him to where he needs to be over the course of the next two or three weeks, so that hopefully he will be available again by the start of February at the latest."
Fabian, 28, came into his own during Kovac's first full season as Eintracht coach. The January 2016 signing from Chivas made 24 Bundesliga appearances last term, producing seven goals and four assists as the Eagles avoided a repeat of the previous campaign's relegation near-miss.
Watch: Fabian's top five 2016/17 Bundesliga goals
Eintracht, who occupy eighth place in the current standings, return to domestic action with a home fixture against Freiburg on Saturday afternoon (kick-off: 15:30CET/14:30GMT).