Russian Potapova's actions were viewed as a public show of support for her country during its invasion of Ukraine and she was criticised by world number one Iga Swiatek.
Potapova, when asked about the shirt after the match, said she had supported Spartak since she was 13 and saw no provocation in it.
"Regarding the Russian soccer team shirt, the WTA has formally warned the player that this was not acceptable nor an appropriate action," the WTA said in a statement. "We do not expect to see any reoccurrence of this in the future."
Ukraine's Lesia Tsurenko withdrew from her match with Belarusian Aryna Sabalenka at Indian Wells due to what she said was a panic attack.
Tsurenko said the attack was triggered by a chat she had with WTA Chief Executive Steve Simon about tennis's response to Russia's invasion. Belarus has been a key staging ground for what Moscow calls a "special military operation."
Russian and Belarusian players can compete on the Tour as individual athletes without national affiliation.
