The probe was opened based on the Criminal Code's article on the desecration of a grave or another place of public respect, the police said in a press release.
Under the article, acts of vandalism in a cemetery or another place of public respect, or desecration of a grave or another place of public respect for racist, nationalist or religious reasons is punishable by community service, a fine or up to three years in prison.
The investigation comes after a video and photos placed on social media platforms last week caused public outrage.
In the video, a Chinese woman is seen removing a wooden cross with a message of support for Hong Kong protesters from its place and throwing it away while laughing.
"Just throw it there," she said in Chinese. "We've done a good thing today. Our Motherland is great!"
A photo shows graffiti on another cross that reads in Chinese, "Hope all cockroaches soon rest in peace. Hope Hong Kong can return to peace."
The video and photo were posted online and translated by supporters of Hong Kong's pro-democracy movement.
Foreign Minister Linas Linkevicius described the incident as deplorable, saying the Lithuanian diplomatic service's further reaction will depend on the outcome of the investigation.