"This has been an incredibly tough decision for me," Matson said in a statement.
"I have enjoyed every minute at Bath Rugby, and we have such a great group of players here who I believe will achieve great success.
"Ultimately, I have made the decision that as a family, we need to be at home in New Zealand, and I appreciate the club's understanding."
Bath opened their Premiership campaign two days ago with a first league win at Leicester for 14 years.
Blackadder said 44-year-old Matson had done an "exceptional" job preparing Bath for the season.
"I know this has been a tough decision for him, but it is a decision we understand and respect," Blackadder said.
"He has made a significant contribution to this club, and as a group we will continue to reap the rewards of his efforts throughout the course of the season."