It follows Tomic and fiery compatriot Nick Kyrgios being warned that their on-court behaviour could threaten their places on the Australian team for the Games in August.
World number 22 Tomic will instead play a low-ranking ATP Tour event in Mexico, which is on at the same time.
"With a heavy sense of regret, I have made the difficult decision to not play with the Australian tennis team as they pursue an Olympic medal in Rio," he said in a statement.
"I make this decision based on what is best for my tennis career," he added.
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The announcement comes after widespread criticism of Tomic's recent on-court attitude and concern over his behaviour by the Australian Olympic Committee.
He made headlines last week when he turned his racquet the wrong way to face a match point in the Madrid Masters first round against Fabio Fognini.
It prompted Australia's Olympic chef de mission Kitty Chiller to call his behaviour in Madrid "appalling".
"Every athlete is under the microscope now," Chiller said after the Australian Olympic Committee's annual meeting last weekend.
"There's a few athletes that are on watch and those two names (Tomic and Kyrgios) are among them."
Tomic has a catalogue of lax commitment in matches, which has earned him the nickname "Tomic the Tank Engine," and he was savaged in the Australian press this week.
"Scheduling can always be difficult in these circumstances," Hewitt told the Australian Broadcasting Corporation.
"Bernie has always made himself available to play for Australia in the Davis Cup and he is very passionate about playing for his country."
Tomic's decision follows two of the country's leading golfers, Adam Scott and Marc Leishman, also opting to give Rio a miss.
Leishman pulled out this month over fears about the Zika virus and its possible impact on his ill wife, while Scott, like Tomic, said he was skipping the event due to a busy schedule.