The mural, one of Rothko's Seagram series, was defaced when a visitor to the Tate applied "a small area of black paint with a brush to the painting," the gallery said.
A photograph posted on Twitter by a gallery visitor showed words, including the name Vladimir, scrawled in the corner of the painting. The gallery, which attracts 5 million visitors a year, was briefly closed Sunday after the incident.
Tate Modern said police were investigating.
The graffiti on the painting also appears to read "a potential piece of yellowism." According to an online manifesto, Yellowism is an artistic movement run by two people named Vladimir Umanets and Marcin Lodyga.
This is not the first time an artwork at Tate Modern has been interfered with. In 2000, two Chinese performance artists attempted to urinate on Marcel Duchamp's urinal sculpture "Fountain."
Rothko, who died in 1970, is renowned for his large abstract paintings featuring bold blocks of color. The defaced painting was one of a series intended to decorate the Four Seasons restaurant in New York. Rothko changed his mind about the commission and gave the works to galleries, including the Tate.
Earlier this year, Rothko's "Orange, Red, Yellow" sold for almost $87 million at auction in New York.