Jordanian border guards surrounded the men, who were attempting to cross the Jordan river valley on Monday.
Local police said they discovered automatic weapons and a large amount of ammunition.
“The vigilance of the border guards foiled their attempt by surrounding the infiltrators, who started to shoot at the guards,” Jordan’s Information Minister, Nabil al-Sharif, told reporters.
Both Israel and Jordan have maintained strict control of their common border.
The last reported incident happened in 2002 and resulted in the death of a man trying to cross into Israel.
The names and nationalities of the four men have not yet been disclosed, AP said.