International stores saw a 7% bump in the month.
May was the second straight month the pizza maker reported the "best sales period" in company history.
And Papa John's says it will continue to provide updates during the pandemic.
"We entered the pandemic with strong growth and momentum, and are fortunate that our delivery and carry-out model has enabled us to meet an essential need for high-quality food, safely delivered to consumers’ homes," Chief Executive Rob Lynch said in a statement.
The company has closed 320 of its 2,100 international franchised stores, with more than a third of those closures, 115, in the Middle East region.
The company's no-contact delivery system and new products are helping drive sales, according to Lynch.
Earlier this month, Papa John's reported that it swung to a first-quarter profit, but missed Wall Street's revenue expectations as the Louisville, Ky., chain contended with the economic shutdown sparked by the coronavirus pandemic.
Papa John's reported net income of $8.4 million, or 15 cents a share, compared with a loss of $1.7 million, or 12 cents, in the year-earlier quarter. FactSet's consensus estimate called for earnings of 39 cents a share.
Papa John's said that on a like-for-like basis with consensus, adding back 26 cents of temporary franchise support that analysts excluded in their estimates, the company reported earnings of 41 cents a share.
Papa John's shares at last check rose 6.5% to near $79.