The Falling Skies actor was taken into custody last month while protesting against Congress's proposed cutting of Medicaid, the US health programme for people and families with low incomes and resources.
Wyle confessed that he was nervous about explaining the situation to his son Owen, but was pleased to find that the child's reaction was positive.
"I did talk to my son after I got released early the next morning," Wyle told People. "I called him before school, and I explained what happened and that I was okay.
"I kind of explained it in as simple terms as possible, and I thought I was going on a little bit too long and I may have lost him, but as soon as I stopped talking, he just jumped in and said, 'I think you did the right thing, Dad'."
Wyle recently described his arrested as "slightly surreal" and stood by the importance of the protests in which he took part.
Wyle's sci-fi TV series Falling Skies returns for its second season in July on FX.