They said the Briton, who was in St Petersburg, was attending the awards ceremony, however.
"I think maybe he’s not coming to the press conference because he’s fed up with always the same questions from the same guys," said Mercedes team boss Toto Wolff when questioned about his driver's absence.
"No, he’s not well. He’s attending the championship celebrations tonight and that’s what matters," added the Austrian.
Ferrari's runner-up Sebastian Vettel and team mate Kimi Raikkonen did attend.
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Wolff said Hamilton had barely made a mistake on track this year but was still looking for ways to improve, and had discussed that on the plane to Russia.
Mercedes are collecting the constructors' championship trophy for the fifth year in a row, a feat only previously achieved by Ferrari.
Under Formula One's sporting regulations, the top three drivers in the championship must attend the prize giving ceremony.
Hamilton has not hidden his dislike of awards ceremonies in the past, while media commitments were also cut back last season.
After the last race in Abu Dhabi in November, Red Bull's Max Verstappen joked that finishing fourth overall in the championship at least meant he would not have to attend the awards ceremony.
"Lucky you," replied Hamilton, who has won four of the past five championships with Mercedes and finished runner-up in the other.
In 2016, his then-world champion team mate Nico Rosberg shocked Formula One by using the pre-awards news conference to announce his retirement from the sport.
(Writing by Alan Baldwin in London, additional reporting by Dieter Rencken in St Petersburg, editing by Toby Davis)
