The Comedy Central show last week ran re-runs on Wednesday and Thursday prompting fears the show might be cancelled. At the time, the network said only that the cancellations were because of "unforeseen circumstances."
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Colbert is expected to address his absence on Monday; His 91-year-old mother, Lorna Colbert, is ill. Colbert's father, James Colbert, and two of his brothers were killed in an airplane crash in 1974.
"My family and I would like to thank everyone who has offered their thoughts and prayers. We are grateful and touched by your concern," Colbert posted on Twitter on Friday.
Comedy Central spokesman Steve Albini told Reuters that Colbert would be back this week, starting with Monday's show with best-selling author Ann Patchett.