Surveillance cameras captured the attack, which happened earlier this month at a Chevron station in the 4900 block of Lakewood Boulevard.
Authorities say the man waited in line at the clerk's register and asked her for a $1.41 Swisher Sweet cigar. The man gave the clerk $1, but when the clerk told him the cigar cost 41 cents more, he argued with her and threatened her.
The suspect then tried to grab the cigar from the clerk, but she pulled away, placed the cigar under the counter and told the man he needed to leave the station.
That's when the suspect leaned over the counter and punched the clerk in her face. He then walked out the door.
The clerk suffered a black eye.
The suspect was described as an African-American man, between 35 and 45 years old, between 6 feet and 6 feet and 4 inches tall, weighing between 215 and 255 pounds. He has short black hair with a slight mustache and a black beard.
If you recognize the man, you're asked to call Los Angeles County Crime Stoppers at (800) 222-TIPS or (800) 222-8477.
City News Service contributed to this report.