Antonelli is one of two drivers to miss media day with an illness.
The other is Cadillac’s Valtteri Bottas, who his team said was “unwell”.
A Cadillac spokesperson said: “The team has taken the decision to allow him a day of rest, to support his recovery.
“This is a precautionary measure and does not currently affect his participation in the remainder of the race weekend. We will continue to monitor the situation and provide updates if necessary.”
On Wednesday, Cadillac announced a new contract for the Finn’s team-mate Sergio Perez, who will stay with the team until at least 2029.
They made no mention of Bottas’ future in the announcement, and are said by insiders to be considering whether to promote their American reserve driver Colton Herta into F1.
Herta is having his fifth outing of the year in practice on Friday at the Autodromo Hermanos Rodriguez, as the team seek to earn him enough mileage to secure the so-called super licence that is required to race in F1.
Herta, previously a front-runner in the US-based Indycar championship, moved to Formula 2 this year with the intention of preparing himself for F1.
His season has not gone well and he is currently 19th in the standings with a best result of fifth place.
However, Cadillac feel he has shown more potential in his F1 outings, which also include a number of runs in cars from previous years.
No decision has been made on whether Bottas or Herta will partner Perez in 2027.