Police said on Thursday that the two men walked into the kiosk in Dortmund, North Rhine-Westphalia, on Sunday at 5am demanding a bottle of Becks Gold.
When the shop worker told them that they did not stock the drink, the two men left.
But 20 minutes later they returned with a jerrycan and after speaking briefly with the shopkeeper one of the men suddenly poured fuel from the can over the entrance to the shop and lit it.
A fire broke out, causing a small amount of damage to the front of the store.
The two men, who police said were drunk, fled. One was described as 175cm tall, 28 to 33 years old with a big nose.
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The other was around 30 years old and 190 cm tall. He was wearing a grey jacket and jogging bottoms. Both spoke in Polish.