The CDC has made no such statement.
An article on social media that makes the claim misuses the unverified material from the Vaccine Adverse Event Reporting System as its source. Anyone can submit a report to VAERS, and those reports are not sufficient to establish whether an adverse event, such as death, was caused by a vaccine.
From December 14, 2020, through March 29, 2021, more than 145 million doses of COVID-19 vaccines were administered in the United States. According to the CDC VAERS received 2,509 reports of death (0.0017%) among people who got the shot.
Although the CDC co-manages VAERS with the U.S. Food and Drug Administration, it is misleading to call VAERS data "CDC data." VAERS reports can be filed by anyone and may include information that is incomplete, inaccurate or coincidental. VAERS is intended to be an early warning system, not a precise measure.