Rustem Umerov issued the appeal via social media on Saturday.
The defence ministry in Kyiv said on Facebook that Umerov was encouraging Polish arms makers to "sign direct contracts" and "set up joint ventures" with Ukrainian weapons manufacturers.
On Friday, Ukraine's defence minister held talks with Poland's top diplomat, Radosław Sikorski, who visited Kyiv to meet with Ukrainian leaders.
During the talks, Umerov "conveyed his gratitude to the people of Poland for the huge assistance provided to Ukraine," the state Ukrainian news agency Ukrinform reported.
Umerov also said he expected "fruitful cooperation" with Poland's new Deputy Prime Minister and Defence Minister Władysław Kosiniak-Kamysz.
Meanwhile, Ukraine's President Volodymyr Zelensky talked with Poland's Sikorski about plans to set up joint Polish-Ukrainian arms factories, according to officials.
The two also "explored the possibility of procuring Polish weaponry, which has demonstrated its effectiveness on the battlefield," Zelensky's aides said.
Later in the day, the Polish foreign minister told private broadcaster TVN24 that domestic firms should "produce more military hardware for Ukraine" and that it could be beneficial for them, Poland's state news agency PAP reported.
Saturday is day 668 of Russia’s war on Ukraine.
Russia invaded Ukraine on February 24, 2022, launching the largest military campaign in Europe since World War II.
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Source: PAP, Ukrinform, president.gov.ua