"Ahmad Robin, 23, died of severe burns that covered more than 90 percent of his body. We could not help him," Issam Shraideh, director of Amman's Bashir public hospital, said on Wednesday.
A YouTube video of the incident on Thursday shows Robin demanding to meet with Social Development Minister Reem Abu Hassan outside the ministry.
"I want to see the minister but she is refusing. I will torch myself to death," Robin shouted, warning police and others around him not to come closer.
The video shows a policeman standing outside the building telling him: "Why are you shouting at me? If you want to burn yourself do it, but keep your distance."
Robin set himself on ablaze and burst into the building as police and others rushed after him.
It was Jordan's fifth self-immolation in less than two years.
The Arab Spring was sparked when Tunisian Mohamed Bouazizi, set himself on fire in December 2010 after police confiscated his cart and prevented him from selling his products.
Jordan has faced sporadic street protests since 2011, demanding political and economic reform as well as a tougher fight against corruption.