"He's ruled out, he didn't travel for tomorrow's game," said Martino about Jimenez, who will be evaluated "day by day."
Mexico will also be without Cesar Montes after the Monterrey defender tested positive for COVID-19.
"In Cesar's case, he's out because he came [to the national team camp] with a positive COVID case, after the game against Cruz Azul," said Tata.
Montes is isolated and recovering in Mexico's High Performance Center (CAR) with the hopes from Martino that "he can overcome COVID and join us" for the game vs. Costa Rica.
Sevilla winger Jesus "Tecatito" Corona will be available for selection, but without the suspended Hirving "Chucky" Lozano and an injured Jimenez, El Tri will once again not be able to utilize the three high-profile players in an attacking setup.
That said, Martino was confident about others who could step up in the frontline.
"This is the Mexican national team, not the national team of only three footballers. We have other players who are very capable of facing this moment," said Martino about the vacancies of Lozano and Jimenez in the match against Jamaica.
With six qualifiers left, Mexico and Martino will need to hold onto their tenuous place in the top three to guarantee themselves an automatic spot to Qatar 2022. El Tri currently sit in third in the Octagonal table, but level on 14 points with fourth-place Panama.
Martino is under pressure after a poor finish to 2021 that included November losses to the United States and Canada in CONCACAF qualifiers. After the disappointing results, he reportedly reconsidered his managerial status with the national team.
Mexican Football Federation (FMF) president Yon de Luisa backed Martino on Tuesday but also stated that there are "no guarantees" for his managerial future. De Luisa also stated that "we'd be very happy" if El Tri are able to get seven or more points in the current three-game international window.
Following Thursday's match, Mexico will then host Costa Rica on Jan. 30 and Panama on Feb. 2 at the Estadio Azteca for the remaining two of three qualifiers.
Initially set to be played behind closed doors due to previous instances of anti-gay chants in the stands, the February matches at the Azteca will now be held to a limited capacity of 2,000 after the FMF won an appeal this month from the Court of Arbitration for Sport. Through the 2,000 that will be in attendance, the FMF will test out new measures regarding fan behavior protocols.