Unable to deliver all its packages in time for Christmas, ​​FedEx Corp.​ said drivers were ​working extra shifts Friday to help the company manage a surge in online shopping as well as severe weather during one of the busiest weeks of its year.

“FedEx Express continues to run limited delivery operations in some markets to deliver shipments that couldn't be delivered before Christmas due to unforeseen volume and severe weather in some areas of the country,” a FedEx spokeswoman said Friday afternoon. She declined to say how...