Gottlieb, who is white, said she was stopped in Denver from boarding a flight to Oakland and asked to prove the boy was her child despite having his passport.
Gottlieb shared her experience in a series of tweets, calling the experience "demeaning and insensitive," adding that they would have missed their flight if it was not delayed.
"I'm appalled that after approx 50 times flying with my 1-year-old son, ticket counter personnel told me I had to 'prove' that he was my son, despite having his passport," she tweeted.
She was told she was stopped because the two have different last names, but Gottlieb believes the incident happened because of their different skin colors.
The agent eventually let Gottlieb check in with her baby.
Southwest later apologized in a statement, and Gottlieb accepted.