The source says their issues "erupted" this past week, resulting in Chmerkovskiy's refusal to rehearse with Lachey in preparation for Monday's episode.
"It was nothing specific, just little disagreements that escalated," the source says.
However, the source notes that Chmerkovskiy will be back next week.
"He'll have to put his ego aside because there are contracts involved," the source says. "He can't just walk off and leave her hanging. One week, sure, he can just say 'personal problems,' but he'll be back next week."
A DWTS spokesperson also tells ET, "Maks and Vanessa are returning to rehearsals and will be dancing together on next week's show."
Meanwhile, on social media, there appears to be nothing but love between the two partners. On Monday night, Lachey Instagrammed that she "can't wait" to dance with Chmerkovskiy again.