The meeting took place in Tehran on Sunday.
Amani, who was injured in pager explosions in Lebanon in September, briefed the Supreme Leader on his health conditions.
The Israeli regime carried out the explosions on September 17 when pagers used by Hezbollah members went off in different regions of Lebanon, leaving dozens of people dead including civilians.
One of the blasts happened near the Iranian ambassador, causing injuries to him, including to his left eye.
Amani was soon transferred to Tehran to receive medical treatment.
He is still in Tehran and will soon return to Lebanon to resume his diplomatic mission.