Warren told reporters in response to the meme that the president should instead spend "his time getting the government back open."
The president posted a meme that referred to the percentage of Native American heritage that a private DNA test discovered.
Warren did not find it as humorous as the 46,000 people who retweeted it did.
"We're now in the 13th day of the shutdown, we have hundreds of thousands of federal employees not getting their paychecks and work that's not being done all around this country," said Warren. "Those are the issues we need to worry about, and that's where we need to focus."
The progressive Democrat had announced on New Year's Eve that she was going to challenge the president in his re-election bid in 2020.
The disastrous political stunt has been panned by her critics, but also by her allies, who saw it as hindrance to her presidential aspirations, instead of the boon that she hoped it would be.
When asked how she will deal with the continuing mockery from Trump, Warren responded that the president "can bluster forever, but it doesn't change the underlying reality."
"Across this country wages are flat, across this country the cost of health care, the cost of sending your kids to college, the cost of housing, the cost of retirement are going up, up, up," she continued. "Those are the things that matter to hard-working families, and the reason that those things are happening are because of bad decisions being made right now in Washington."
In response to the DNA debacle, Warren later admitted that she was not a "person of color."