Sufian Abu Nada told a Palestinian radio station Monday that his 21-year-old son Ihab set himself alight after he urged the young man to find work.
Sobbing, Abu Nada said the family was struggling to get by on $220 a month.
There have been dozens of similar copycat deaths throughout the Middle East since a Tunisian man set himself on fire in December 2010, helping trigger the mass protests that have swept across the Arab world.
But Sunday night's incident was the first time in the Islamic militant Hamas-ruled Gaza Strip.
Gaza has fallen into deep poverty resulting from international isolation and an Israeli-led blockade of the seaside strip.