Voting began at 9 a.m. in each country, local time, and was scheduled to last through Sunday, Aswat Masriya reported.
Roughly 681,000 Egyptian expatriates in 161 countries were eligible to vote.
Egyptian Foreign Minister Nabil Fahmy said a team in Cairo was appointed to monitor the voting process.
The amended constitution was written by a 50-member assembly and President Adli Mansour called for a public vote to approve it. Domestic voting is set for Jan. 14-15.