The award was given in recognition of Gen Bajwa's "distinguished efforts in strengthening UAE-Pakistan ties and his role in consolidating bilateral co-operation between the two friendly countries", news agency Wam reported.
The Order of the Union is the second-highest honour awarded by the UAE to senior officials of friendly nations.
During the meeting, the pair discussed bilateral co-operation and joint action in areas of defence to serve mutual interests.
They also exchanged views on the latest regional and global issues and developments of mutual concern.
Sheikh Mohamed bin Zayed spoke about the deep, longstanding relations between the UAE and Pakistan and the mutual keenness to continue strengthening them at various levels.
He appreciated efforts made by Gen Bajwa to develop prospects for co-operation and joint work between the two countries.
Gen Bajwa expressed his thanks and appreciation to the UAE president and spoke of his pride in receiving the honour, which he said reflects the strength of the friendly relations. He said his country is keen to develop and advance its co-operation with the UAE.