The snapshot is the first to be made public since Musavi was put under house arrest in February 2011 for challenging Iranian leaders.
The origin of the photo is not clear. It was published on the opposition website Kalame, which is close to Musavi, and which praised the opposition figure for his resistance in the face of the state pressure he's been facing. The website said the photo was not taken "in recent days."
Kalame said Musavi has become a "compassionate father" for all Iranians.
The photo seems to have been taken at a hospital. It shows Musavi lying in bed while presumably talking to someone standing in front of him.
Nargess Mosavi, one of Musavi's daughters, posted the photo on her Facebook page along with a Father's Day wish.
"Happy Father's day to all those who are fathers, be it in jail, at home, under the ground, or those who have been martyred for freedom," she wrote.
Musavi's relatives and supporters have expressed increasing concern over his health in recent weeks.
He has reportedly been hospitalized several times in a span of several months for heart problems.
"Kalame" reported last month that Musavi had undergone an angioplasty.
Musavi, his wife Zahra Rahnavard, and reformist cleric Mehdi Karrubi were put under house arrest more than three years ago, after their calls for a demonstration in solidarity with the uprisings in Egypt and Tunisia attracted tens of thousands of opposition members.