Julija Samorokovskaja, a spokeswoman for the capital's police, told BNS that someone had apparently poured acid on the monument in Zydu Street in the past two days.
A guide reported the act of vandalism to the police on Sunday evening, she said.
A pre-trial investigation into incitement to hatred has been launched, according to the spokeswoman.
The monument was doused in some light liquid in late June. Samorokovskaja said the police investigation into the incident was underway.
The monument to Doctor Tsemakh Shabad, who inspired Korney Chukovsky to create the popular children’s stories character Doctor Aibolit, in the Old Town's Mesiniu Street was also vandalized back then.