All six victims were taken to hospitals, where they are receiving medical treatment, Lysak said.
Initial reports had put the number of injured at three before authorities updated the toll.
Explosions were heard in Odesa at around 5:35 a.m. Ukraine’s Air Force had earlier warned that cruise missiles were heading toward Odesa Oblast.
Russian forces attacked Ukraine with missiles and drones overnight on Sept. 12, with explosions also reported in Dnipro, Kryvyi Rih and Zaporizhzhya.
In Kryvyi Rih, Russian forces struck an industrial facility, killing one person and injuring two others.
In Zaporizhzhya, a Russian drone destroyed a private house, killing a 64-year-old woman and a 37-year-old man.
A 59-year-old woman was injured in the attack, which also sparked a fire at the site.