Paraguayan left back Bruno Valdez, who scored America's equaliser in the 67th minute, crashed into Gignac's back in the 76th and the Frenchman was carried off and taken to hospital where he was put in a neck brace.
"When there is a cervical sprain, when there is damage to the ligaments that steady the neck … there is no way they can recover in less than two weeks," D'Acosta told the sports website Record (www.record.com.mx).
Tigres have said Gignac is doubtful for the match in Monterrey.
Gignac, top scorer in the Apertura with 17 goals, is looking to win his second LIGA MX title in his second season with Tigres. They are chasing a fifth league crown, while America are seeking a record 13th.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
The final was postponed from mid-December because America were taking part in the Club World Cup in Japan.
(Reporting by Rex Gowar; editing by Martyn Herman)
