Rouhani said in a speech on Saturday the UAE had made a "huge mistake" in reaching an agreement to normalize ties with Israel and called it a betrayal by the Gulf state.
"They (the UAE) better be mindful. They have committed a huge mistake, a treacherous act," he said of the agreement announced on Thursday.
The UAE foreign ministry said the speech was "unacceptable, inflammatory, and carrying serious repercussions for the security and stability of the Arabian Gulf region", the statement carried by WAM said.
The chargé d'affaires has been given a "strongly worded memo," WAM said.
There was no response yet from Tehran.
The UAE statement said the ministry considers Rouhani's speech interference in UAE internal affairs and an assault on its sovereignty.
The foreign ministry reminded Iran of its duty to protect the UAE diplomatic mission in Tehran.
To protest the UAE-Israel agreement, a small group of Iranians gathered in front of the UAE embassy in Tehran late on Saturday, Iranian media reported.
The US-sponsored deal has been seen as firming up opposition to regional power Iran, which Gulf states, Israel and the United States view as the main threat in the conflict-riven Middle East.The UAE, which is home to thousands of Iranians, says it pursues a de-escalatory policy towards its neighbor Iran.