Earnhardt wrote on Twitter that all Americans are granted the rights to "peaceful protests" before quoting former President John F. Kennedy.
"Those who make peaceful revolution impossible will make violent revolution inevitable," Earnhardt wrote.
At a rally in Alabama last Friday, Trump suggested that NFL owners should fire players who protest the national anthem.
"Wouldn’t you love to see one of the NFL owners, when somebody disrespects our flag, to say 'Get that son of a b---- off the field right now?'" the president said.
In response, NFL owners took a unified stand against Trump's comments at the start of several games on Sunday.
Several NASCAR team owners and executives said Sunday that they would not want anyone in their organization to protest, The Associated Press reported.
Among them was Richard Childress -- the longtime team owner for Earnhardt's father -- who said protesting would "get you a ride on a Greyhound bus," according to the AP.
"Anybody that works for me should respect the country we live in," Childress said. "So many people gave their lives for it. This is America."
Earnhardt has spoken out against the president's policies in the past. In January, the legendary NASCAR driver had a Twitter conversation with a fan in response to Trump's immigration ban, saying that "America is created by immigrants."
"[My] fam immigrated from Germany in 1700s escaping religious persecution," Earnhardt said.
In April, Earnhardt, 42, announced that he would retire at the end of the year after driving for 18 seasons and competing in more than 600 races.