"The states of the Gulf Cooperation Council consider what happened in Sanaa on Tuesday... A coup against the legitimate authority," the ministers said in a statement following an emergency meeting in Riyadh.
The GCC also expressed support for the "constitutionally legitimate authority" of Hadi, and rejected "all measures aimed at imposing change by force".
They warned that Gulf states "would take all measures necessary to protect their security, stability and vital interests in Yemen."
They also called for the withdrawal of militiamen around Hadi's residence in western Sanaa.
Gulf countries had brokered an accord in November 2011 that eased former president Ali Abdullah Saleh out of office following a year of nationwide protests.