The Olympic soccer player was furious after Chmerkovskiy grabbed her shoulder during rehearsals in an attempt to make a point when he became frustrated with her struggle to grasp a new routine for the show two weeks ago.
"Outside of the cameras, [Maks] knows that he was in the wrong. He will be the first one to stand up to that," Solo said during an interview on Ryan Seacrest's KIIS-FM radio show.
"I almost quit the show right then and there. I almost walked out, but I told myself I am in this for the long-haul, through all the bumps and bruises. You can tell I didn't really flinch."
However, Solo reiterated that she would never allow such an incident to go unresolved, adding: "I want everybody to know out there that as a strong, independent woman that stands up for herself, I would never just let that go unnoticed."
Chmerkovskiy caused controversy last month after arguing on air with judge Len Goodman, saying that he should retire from the industry.
He later refused to apologise for the outburst but has insisted that he feels lucky to be part of the Dancing with the Stars family.