Maciej Wewiór told reporters in Warsaw that 110 people requiring medical assistance were expected to arrive overnight in the Polish capital aboard two Polish military aircraft.
He said passengers were boarding in Muscat, the capital of Oman, and that the military planes had arrived shortly before the evacuees reached the airport to minimise their time on the ground.
Wewiór said Polish consuls accompanied citizens travelling by bus from the United Arab Emirates to Oman, helping them cross the border.
The buses were organised by consular officials with support from a Polish state-owned company, he added.
He said the ministry had no information that any Polish citizen had been injured in connection with the fighting in the Middle East, though the situation varied from country to country.
Airspace over the United Arab Emirates was being reopened temporarily, Wewiór said, estimating that up to 40,000 tourists could depart the country daily.
If the security situation remains stable, the tourism crisis there could ease within a week, he said.
If the reopening continues gradually, up to 100 flights per day could operate, he told reporters, adding that Polish authorities were working to ensure that as many of those connections as possible include flights to Poland.
Wewiór said a crisis team met on Thursday at the foreign ministry in Warsaw under the leadership of Sports and Tourism Minister Jakub Rutnicki to discuss the situation, including in countries beyond the Persian Gulf and Arabian Peninsula.
He said that only a handful of Polish citizens still wanted to leave Israel, and that no Poles in Lebanon or Jordan had expressed a desire to depart.
Wewiór said a consular official in Dubai remained available around the clock and that a special hotline launched on Sunday for Poles in the Middle East had received more than 3,000 calls.
He appealed for the line to be used only by those in need of assistance, saying some callers had posed as journalists and attempted to record or test the service.
On Wednesday, Prime Minister Donald Tusk announced he had decided to deploy military aircraft to support the evacuation.
President Karol Nawrocki, who serves as commander-in-chief of Poland's armed forces, approved the use of a Polish military contingent to assist with evacuations from Saudi Arabia, Bahrain, Egypt, Israel, Qatar, Kuwait, Oman and the United Arab Emirates.
Under the decision, up to 150 troops may be deployed between March 5 and March 31 to assist in evacuating Polish citizens, particularly those requiring medical support.
The evacuations follow attacks by the United States and Israel on Iran on February 28 and subsequent retaliatory strikes by Tehran, which prompted many airlines to cancel flights across the region.