"We will have to strengthen our forces on this section of the border and also consider ... building similar border fortifications to those we now have on the Polish-Belarusian section," he said.
Russian media has reported that Kaliningrad has opened its skies to flights from the Middle East and Asia in a bid to attract more airlines and tourists.
"After what we had to deal with, and are still dealing with on the Polish-Belarus border, and considering the opening of the skies above the Kaliningrad region for aeroplanes from Turkey, Syria and Belarus, it could be in the coming weeks," Sobolewski later told Reuters, referring to increasing arrivals of migrants.
Kremlin spokesman Dmitry Peskov told reporters in a briefing that Russia would not interfere with any such decision.
"History proves the stupidity of decisions to build walls every time, because over the years or decades, all walls fall," he said.
Sobolewski said there were signs of larger groups of migrants appearing at the Belarus border.
Poland has built a 5.5 metre (18 feet) tall steel barrier, equipped with motion sensors and cameras, stretching for about 187 km (116 miles) on the Belarus border.
Poland had previously said that the border guard had received funds to build an "electronic barrier" of sensors and cameras on the Kaliningrad border.
