The actress told Channel 4’s Steph’s Packed Lunch she fell ill after going to the theatre with five other people, who all also later fell ill.
Atkinson, who tested positive for the antibodies in March, said everyone in the group displayed different symptoms.
“The only thing we had in common was we all lost our sense of smell and taste,” she said.
She added that her stepfather Peter “was really poorly” and was in bed for two weeks.
Atkinson also discussed the extensive testing regime her partner Gorka Marquez is undergoing for Strictly Come Dancing ahead of the new series of the programme.
She met the professional dancer when she competed on the series in 2017.
“They’re doing tests all the time,” Atkinson said.
“They’re doing the bubbling and then he gets two weeks off, but again he has to isolate.
“Then they’re doing more tests before they go back.”
Boxer Nicola Adams, DJ Clara Amfo, former home secretary Jacqui Smith, actress Caroline Quentin, comedian Bill Bailey and reality star Jamie Laing are among the celebrities starring in the upcoming series.