Hans-Joachim Watzke underlined his concerns after Bayern agreed a deal to extend their partnership with the financial services provider.
Allianz, who already own the naming rights to the Bundesliga champions' stadium, acquired an 8.33 per cent stake in the club in exchange for a sum of €110 million.
It leaves Allianz with the same percentage share as adidas and Audi, with Bayern stating that the money would be used to pay down the "remaining obligations on the Allianz Arena" and the "planned reconstruction of the youth and junior facility in Munich".
However, Watzke is worried that the financial boost will see Bayern increase their stranglehold on the German top flight.
"This development was predictable," he told Bild.
"They've been negotiating with Allianz for a long time and I can only congratulate them on the deal, but the gulf to the rest of the Bundesliga is obviously going to grow further because of it."
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