The embassy did not say what evidence it had for the attack in a statement posted on its official Twitter site and its Facebook page.
Ukraine's general prosecutor's office said it had opened an investigation into the alleged incident.
Russia has called its military actions in Ukraine a "special operation".
It denies targeting civilians and says its air strikes, ground and sea offensive are intended to destroy Ukraine's military infrastructure.
Ukraine and its allies have accused Russia of targeting civilians indiscriminately.
Thousands of people have been killed during Russia's invasion, which began on February 24, and several million have been displaced.
"Today, Russian forces shot and killed 10 people standing in line for bread in Chernihiv. Such horrific attacks must stop. We are considering all available options to ensure accountability for any atrocity crimes in Ukraine," the US embassy said.
Russian defence ministry spokesman Igor Konashenkov said the report and footage of alleged victims that had appeared in various Ukrainian outlets was a "hoax launched by the Ukrainian Security Service".
"No Russian soldiers are or have been in Chernihiv. All units are outside of the Chernihiv city limits, blocking roads, and are not conducting any offensive action," he said, adding that the US embassy had published an "unverified fake".
