Ukraine's federation and its commercial partner UFI have set prices for the match in Donetsk at $25-$1,000 per ticket, according to media.
This is far too expensive for many Ukrainians who have been hit hard by the global economic crisis.
Akhmetov, billionaire owner of the Donetsk stadium Donbas Arena, urged the Federation to buy up all the tickets at a reduced price and then sell them to fans at a discount.
But the Federation refused, accusing him of a "cheap propaganda trick."
"Unfortunately, your mind and conscience are guided by the opportunity of earning $4.6 million. To my great sorrow, you are not bothered about whether Donbas Arena will be full or not on 18 November," Akhmetov's Shakhtar website quoted him as saying.
"I had been expecting you to make a wise decision that would allow the supporters to buy tickets at the reasonable prices and the national team of Ukraine to feel the thundering support and atmosphere of overcrowded home ground at the decisive match."
The Federation, headed by tycoon Hryhoriy Surkis, said Akhmetov's proposal was "unreal" and "absurd".
"Public promises by the leadership of Shakhtar to help fans ... is a cheap propaganda trick," its press-service said in a statement.
"The Federation thinks that a statement by the Shakhtar president is further confirmation of his real task ... to make impossible the proper carrying out of the Ukraine-Greece game."
Media said that only 50-60 percent of the tickets had been sold so far.
The first leg of the playoff ended 0-0 in Athens on November 14. The winners of the tie qualify for next year's finals in South Africa.
