The attack early on Wednesday was one of the deadliest on western Ukraine since Russia’s full-scale invasion began in February 2022.
Zelensky said there had been “significant destruction” in Ternopil, adding that people could be trapped under the rubble.
Energy facilities, transport and civil infrastructure were damaged elsewhere in western Ukraine.
The energy sector in Ivano-Frankivsk region was also attacked, and two of the three injured were children.
Critical infrastructure and energy were hit in the Lviv region, Zelensky said, while the head of the region said a energy facility had been struck.
Zelensky, who is in Turkey for talks with his counterpart Recep Tayyip Erdogan, called for aid from Ukraine’s allies, writing: “Every brazen attack against ordinary life shows that the pressure on Russia is insufficient. Effective sanctions and assistance to Ukraine can change this.”
Ukraine’s president had said he wanted to “intensify” peace negotiations ahead of the meeting in Ankara, but the Kremlin said no Russian representative would join.