He and his partner, Katya Paquin - a former Green researcher and sister of True Blood star Anna - had a baby daughter in December, a sister for their two boys aged under 5. Ms Paquin and the baby are understood to be in good health.
Dr Norman said he had been thinking of standing down for some time and wanted to take the summer break to consider the decision.
He had not decided whether to leave Parliament altogether after his replacement had been elected.
But it seemed clear yesterday that he would consider working outside politics if the right job came along.
If he stays on in Parliament, he will take a pay cut of almost $20,000 in leadership add-ons that he shares with co-leader Metiria Turei.
He sparked a diplomatic incident in 2010 when he used his position as an MP to get close to Xi Jinping, then vice-president of China, in what was meant to be a protest with a Tibetan flag but which ended in a scuffle with Chinese security staff.
Dr Norman made a big impact last term as the party's finance spokesman, especially in the area of green technology. Labour had vetoed finance for Dr Norman but it was preparing to give him an important portfolio had it been leading a coalition government this term.
The Australian-born 47-year-old political activist came to New Zealand to do a PhD on the Alliance, of which the Greens were a member. He stayed and ended up working for Sue Bradford when she was a Green MP.
He was not actually an MP when he was elected the male co-leader after Rod Donald's sudden death.
Joking at his press conference yesterday he said the hardest part about living in New Zealand was not really knowing anything about sport.
"I've always lived in fear that someone would ask me a sports question [and] I'd have no idea, but that didn't happen actually so I've kind of got away with it."
Nominations for the co-leadership position will open on March 20 and close on April 17.
Nominations are open to any financial member but the role is likely to go to an MP.
The male MPs are: Steffan Browning, David Clendon, Kennedy Graham, Kevin Hague, Gareth Hughes and James Shaw.
Big boots to fill
The possibles:
• Kevin Hague - West Coast-based MP since 2008. Highly respected across parties.
• James Shaw - Wellington-based MP since 2014. Business friendly but a real political novice.
• Gareth Hughes - Wellington-based MP since 2010, tech savvy, strong campaigner, new generation.