He scaled the walls of Ajram’s villa in the Keserwan district of Mount Lebanon early in the morning and evaded three security guards before entering the property, according to media reports in Beirut.
Once inside, the intruder was confronted by Ajram's husband, celebrity dentist Fadi Al Hashem, who shot and killed the man before police arrived.
According to Lebanon's state run National News Agency, an arrest warrant was issued on Sunday for Al Hashem and an investigation is under way.
Ajram has yet to make an official comment about the incident but it is thought that she and her three children were in the house at the time of the shooting.
Lebanese broadcaster MTV has aired footage allegedly showing the robbery. It said the video was taken from one of the security cameras inside Ajram's home.
It shows the attacker pointing a gun at Al Hashim. After a brief exchange between the men, the footage cuts to the intruder making his way to one of the rooms. A few seconds later, Al Hashem appears with a gun and chases after the man.
The footage ends with Al Hashem shooting at a figure not seen on screen.
Reports suggest the intruder was a 30-year-old Syrian called Mohamed Hasan Al Mousa.
News of the incident went viral on regional social media channels, with Ajram’s peers and fans rallying in support of the singer.
“Thank God for your safety and your family and daughters,” Lebanese singer Elissa said. “I can't imagine what an ugly thing has happened. Thank God, you are okay. May God protect you and your family.”
Emirati-Yemeni singer Balqees tweeted: “Thank God for your and your family's safety. May God protect you from all harm.”
Lebanese singer and actress Cyrine Abdelnour expressed her dismay over the incident. “Frankly, I can't comprehend how heinous this news is. We thank God you and your family are safe and may God protect you and us from all this chaos.”
Ajram's most recent live performance was a free New Year’s Eve concert on Abu Dhabi’s Al Maryah Island.