Dodon's move on Wednesday underscores divisions within the ex-Soviet nation, where the president is frequently at odds on foreign policy with the government, which favors closer ties with the European Union and the United States, Reuters said.
The government had planned to send 57 servicemen to take part in exercises by mostly NATO countries, including the United States and Turkey, in western Ukraine from Sept. 8-23.
Russia will meanwhile hold drills from Sept. 14-20 in western Russia, Belarus and Russia's exclave of Kaliningrad. Moscow has dismissed fears in neighboring nations that the drills may be used as a precursor for an invasion.
Read alsoMoldova's president: Transnistria will never become federal subject of RussiaDodon exercised his presidential veto to block the decision, arguing Moldova was bound by its constitution to stay neutral.
"The participation of Moldovan servicemen in military exercises outside the country is not acceptable," Dodon wrote on his Facebook page.
A Ukrainian defense ministry spokesman said Kyiv had not been formally notified that Moldova was withdrawing its personnel.
Earlier this year Dodon banned the participation of military personnel in NATO exercises in Romania, prompting complaints by the U.S. and Romanian ambassadors in Chisinau.
Speaking at a televised cabinet meeting, Prime Minister Pavel Filip said he was baffled by Dodon's decision: "No one wants an unprepared and weak army."
Moldova has been governed by pro-Western leaders since 2009 and signed a trade pact with the EU in 2014. Russia retaliated by halting imports of Moldovan farm produce, depriving the country of a key market for its wine, fruit and vegetables.
Relations suffered further this year due to a dispute in March over the treatment of Moldovan officials traveling to or through Russia, and the expulsion of Russian diplomats in May.
In August, Moldova declared Russian Deputy Prime Minister Dmitry Rogozin persona non grata, accusing him of making defamatory remarks about Moldovan government officials.