"We saw a lot of Republican legislatures across the country do everything they could to inhibit poor people and people of color from participating in a democratic process," Abdul-Jabbar told CNN's Poppy Harlow on Sunday. "And that has resulted in what we have to deal with now."
Abdul-Jabbar's concerns echoed those recently brought by NAACP President Cornell William Brooks, who last week said on CNN the Voting Rights Act needs to be fixed.
Parts of that law, passed during America's civil rights movement in 1965, were struck down by the US Supreme Court in 2013.
"I'm not doing anything to try to inhibit Mr. (Donald) Trump from governing -- that is his job now," Abdul-Jabbar said. "I do hope that people who were disenfranchised in the process of the campaign get their voting rights back, because we will definitely have to have a reckoning on this."
Abdul-Jabbar has been an outspoken political advocate and backed Hillary Clinton during the election, and spoke at this year's Democratic National Convention.
After Donald Trump's victory last Tuesday, the former NBA star penned a column for the Washington Post about what it means to be black during a Trump administration.
While the country is "supposed to come together after an election," Abdul-Jabbar wrote, "it's difficult to link arms when the home of the free embraces the leadership of a racist."
In that column, Abdul-Jabbar also hammered what he called Trump's "disconnect from black people and black culture."
"For African Americans, America just got a little more threatening, a little more claustrophobic, a lot less hopeful," he wrote. "We feel like disposable extras, the nameless bodies who are never part of the main cast."
Race relations have also been at the forefront of Abdul-Jabbar's advocacy. In response to ongoing tensions between black communities and police, he tweeted this summer that both live in fear "because they cannot see each other's humanity."
Speaking on CNN on Sunday, Abdul-Jabbar said he hopes the country can now turn its focus "to understand and appreciate our fellow citizens and communicate with them in a way where we can solve problems."