Mallya has yet to attend a grand prix this year, absent from the season-opener in Australia and Bahrain, and the team said the 60-year-old never had any intention of travelling to Shanghai for Sunday's third round.
"He does not usually attend this race," said a team spokesman after the day's free practice sessions.
Mallya's immediate whereabouts were unclear and he was not available for comment.
Deputy team principal Bob Fernley told Reuters this month that Mallya, who is a member of the upper house of India's parliament, had no plans to travel to any races until the Spanish Grand Prix in Barcelona on May 13-15.
That follows on from Russia as the fifth round of the championship and start of the main European season.
The beer baron's financial problems have been mounting steadily and he left India last month amid pressure from lenders to repay about $1.4 billion in debt owed by his defunct Kingfisher Airlines.
On Friday, India's foreign ministry gave Mallya a week to answer why his passport should not be impounded or revoked.
Force India's other main co-owner is the Sahara conglomerate, whose founder Subrata Roy was arrested in March 2014 after the company failed to comply with a court order to refund money raised from millions of small investors.
"Obviously money isn’t lavished upon us but the team has done very well over the last few years in constantly moving up and increasing its revenues from the constructors’ championship," Fernley told Reuters after Bahrain.
"We actually have a significant amount of revenue coming in from the commercial side and we are pretty close to being self-sufficient.
"Diageo signed a contract with us earlier in the year for five years so it’s a significant programme. It’s for Smirnoff, which is still on the car," he added.
The team finished fifth overall last season, their best ever showing, and Mexican driver Sergio Perez also brings substantial backing from sponsors.
Fernley and chief operating officer Otmar Szafnauer share the duties of running the team at race weekends in Mallya's absence.
(Reporting by Alan Baldwin, editing by Toby Davis)
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