Mr Rivera, a regular contributor on the conservative news channel, made the claim on the morning after Martin Luther King Day in a segment addressing the president’s appearance at the World Economic Forum in Davos.
The guest told Fox & Friends he felt “awful” for Mr Trump because the president has had to answer question about his impeachment trial at the summit.
“This is an economic summit. The American economy is the envy of the world,” Mr Rivera said.
“I call him, to great controversy, a civil-rights leader, especially yesterday on Martin Luther King Day.”
He explained: “African American unemployment - lowest it’s ever been. Latino unemployment - lowest it’s ever been. This rising tide is lifting all boats, we should be celebrating.”
Although both measures have increased in recent months, it is true that the African-American and Hispanic unemployment rates have reached record lows in 2019 – at 5.4 per cent in August and 3.9 per cent in September respectively – according to official statistics.
In December, African-American unemployment was at 5.9 per cent, while Hispanic unemployment was at 4.2 per cent.
Those figures have continued a long-running downward trend in African-American and Hispanic unemployment rates that began during the Obama administration, following an increase after the 2008 financial crash.
Mr Trump has often touted low levels of African-American unemployment as one of his major achievements and even mentioned it in a tweet for Martin Luther King Day.
On Monday, the president appeared to liken himself to the civil rights leader as he boasted about low unemployment figures.
"It was exactly three years ago today, January 20, 2017, that I was sworn into office. So appropriate that today is also MLK jr DAY," he wrote.
"African-American Unemployment is the LOWEST in the history of our Country, by far."
However, the president’s record on civil rights has repeatedly come under criticism from activists and campaigners.
In November, the FBI reported that violent hate crimes and threats in the US had reached their highest levels in 16 years, partly due to a surge in attacks on Hispanic people in 2018.
Activists and civil rights researchers have said Mr Trump’s hardline anti-immigration policies and controversial verbal attacks on Latino immigrants carried some responsibility for the rise.
“President Trump frequently refers to Latinos in the most hateful and bigoted ways, and words matter,” Janet Murguia, head of the Washington-based Latino civil rights organisation UnidosUS, said.
“Having just visited El Paso [after the mass shooting in August] and hearing first-hand from the victims of the tragic shooting there, I know that hateful words have hateful consequences, and can result in violence and even death.”
The president also faced widespread criticism in July when he suggested four congresswomen of colour, three of whom were born in the US, should “go back and help fix the totally broken and crime infested places from which they came”.
Many commentators said Mr Trump’s statement was racist - including Mr Rivera, who told The New York Times: “As much as I have denied it and averted my eyes from it, this latest incident made it impossible.”
“I do insist that he’s been treated unfairly. But the unmistakable words, the literal words he said, is an indication that the critics were much more right than I,” Mr Rivera added.