Hollande made the announcement on Wednesday in a televised statement, saying he was "closing the constitutional debate".
The proposed reforms had failed to find agreement in the lower house, the National Assembly and the opposition-dominated Senate, and looked unlikely to pass.
"A compromise appears out of reach on the stripping of terrorists' nationality," Hollande said.
Hollande had proposed to constitutionalize exceptional security measures, including stripping convicted terrorists of their nationality, shortly after suicide bombers and gunmen from the Islamic State armed group killed 130 people across Paris last year.
The move would have seen convicted terrorists with dual nationality stripped of their French passports and deported.
The controversial proposal had deeply split his own Socialist government and was opposed by the centre right opposition.
During his announcement on Wednesday Hollande said he took note that "a section of the opposition is hostile to any constitutional revision. I deeply regret this attitude," he said.
The French president added he would not deviate from commitments to “ensure the security of our country”.
Any changes to France’s constitution must be approved by three-fifths of French MPs and senators. A special Congress of Versailles of all parliament members had been due to consider the issue next month.
Nicolas Sarkozy, the leader of the opposition Républicains party, said Hollande "created the conditions for [the proposal's] failure."