Tabloids Expressen and Aftonbladet gave thumbs down to the Aug. 3 concert at Ullevi stadium in Goteborg, with Expressen suggesting Richards was "superdrunk" on stage.
"This is a first!" the 63-year-old rock star wrote in a letter published by Stockholm daily Dagens Nyheter. "Never before have I risen to the bait of a bad review.
"But this time ... I have to stand up ... for our fans all over Sweden ... to say that you owe them, and us, an apology."
Dagens Nyheter said it received the letter from concert organizer EMA Telstar. Company head Thomas Johansson told The Associated Press that Richards wrote the letter and gave it to him after reading translations of the Swedish reviews.
"There were 56,000 people in Ullevi stadium who bought a ticket to our concert - and experienced a completely different show than the one you 'reviewed,"' the letter said.
"How dare you cheapen the experience for them - and for the hundreds of thousands of other people across Sweden who weren't at Ullevi and have only your 'review' to go on.
"Write the truth. It was a good show."
In his review, Aftonbladet's music writer Markus Larsson gave the concert a score of two on a five-point scale, and said Richards appeared "a bit confused."
"I am not going to apologize for my subjective opinion," Larsson told the paper's Web edition on Wednesday. "It is Keith who should apologize. After all it costs around 1,000 kronor (EUR107; US$145) to see a rock star who can hardly handle the (guitar) riff to 'Brown Sugar' any more."