"Border police carried out an operation this morning in a cemetery in Petah Tikva looking for foreigners residing in Israel illegally," Luba Samri said.
"For reasons that are still unclear, a border policeman opened fire on an illegal resident, a Palestinian, who was there, and killed him," she said.
Israel requires that all Palestinians from the occupied territories apart from annexed Arab east Jerusalem have permits to be in the country.
The number of permits issued has dwindled to a trickle since the second intifada, or uprising, of 2000 to 2005.
Last year, Israel launched a crackdown on what it said were 60,000 illegal immigrants from Africa, rounding up and deporting 3,920 by the end of 2012, and building a high-tech fence along the border with Egypt.
Parliament is mulling new legislation aimed at deporting thousands more migrants whom the government regards as a threat to the Jewish character of the state.