New Green MP Ricardo Menéndez March asked for a special exemption for a place in MIQ and it was turned down.
He needed to travel to Mexico because of a "serious family matter" and his leave was approved by the party, sources told 1 NEWS.
National's Judith Collins told media today she would not have let her MPs travel.
Covid-19 Response Minister Chris Hipkins and Green Party co-leader James Shaw were contacted by the Chief Executive for Ministry of Business, Innovation and Employment Carolyn Tremain as part of the no surprises policy.
Tremain said she called them to ascertain if there was "any information we were missing that would factor in the outcome of the application".
"As a result of both of these conversations, I was comfortable with the decision to decline the application."
Shaw said it was a "very serious family issue" for Menéndez March to travel.
"He had no special treatment, he went through exactly the same process that anybody else doing the same thing would."
Menéndez March was able to secure a place without a special exemption and will finish managed isolation this weekend and is set to be back in Parliament on Tuesday.