Konstantin Senchenko, a local politician in Siberia, had posted criticism of Mr Kadyrov on Facebook.
However, Mr Senchenko then posted a grovelling apology, leading to widespread speculation that he had been forced to do so.
Mr Kadyrov also uploaded a video of Mr Senchenko apologising on to Instagram.
In it Mr Senchenko is seen to say: "I apologise profoundly".
"I was wrong - I let my emotions get the better of me," he adds.
The row began on Tuesday when Mr Kadyrov, an ally of Russian President Vladimir Putin, branded some members of the opposition "enemies of the people and traitors" and called for them to be put on trial.
Mr Senchenko then wrote a Facebook post critical of Mr Kadyrov, calling him a "disgrace to Russia" and saying he should "get lost".
He also implied that Mr Kadyrov was corrupt and ill-educated.
Beneath the Instagram video of Mr Senchenko's subsequent apology, Mr Kadyrov wrote "I accept" - and added five smilies.
His own incendiary statement on Russia's opposition is still displayed on his official website, unaltered, the BBC's Sarah Rainsford reports from Moscow.
Mr Kadyrov took charge of Chechnya with Kremlin support in 2007, and continued a long fight against Islamist rebels.
In exchange for loyalty to Russia, the authoritarian Chechen leader has been allowed to maintain his own security force and has largely had a free hand to run the southern Russian republic as he sees fit.
Human rights groups accuse Mr Kadyrov's security forces of abuses, including torture and extrajudicial killings.
A Russian politician who criticised Ramzan Kadyrov, the Russian-backed Chechen leader, has made a "profound" apology.