A campaign period, including a roadshow around the main centres, would run until Mach 26 and branch delegates would then vote until April 7. The winner would be announced on April 8.
Turei resigned following a firestorm over her revelations of historic welfare fraud when she was on the solo parents' benefit. She had admitted to failing to disclose she had sometimes lived with other people. Turei declined to comment on the contest.
Shaw said he had not yet decided whether he would vote and would not say if he had a preference.
The MPs had agreed not to publicly back any of the candidates – unless they were standing themselves.
Anyone who had been a Green Party member for more than six months was eligible to stand.
Shaw said it would be "pretty unusual" for somebody who was not in Parliament to do the job, but it had happened in the past when Dr Russel Norman was elected after the death of Rod Donald.
"There would certainly be some big logistical challenges that we would have to overcome in order to make that work. But we have done that before."
The party would provide some funding for any candidates who were not MPs to help with travel costs to any roadshow events.
He said non-MPs were at a disadvantage because MPs' travel was covered by the taxpayer. However, otherwise the party would apply the tighter rules of an election campaign to any use of Parliamentary funding by MPs.
Shaw said that cost to the taxpayer and the time it could take MPs away from their job were other reasons for a shorter campaign period than in the past.
The last contest was spread over five months.
"Last time it did drag on and I think it did distract some of us for an unnecessarily long period of time. We want to minimise that cost.
Now we are in Government we have to stay focused on the business at hand and so we want to get this out of the way."
There were no restrictions on advertising, but candidates would have to pay for it themselves.
Donations of more than $500 would be disclosed to the party but not publicly, although MPs would have to include them in the annual Register of Pecuniary Interests.
Co-leader elections usually take place at the party's annual general meeting but Shaw said the party did not want the role left vacant for almost a year so decided to go earlier.
He defended the co-leadership model, saying every model had pros and cons and he was happy with them.
Shaw said the party was aware of the risk unsuccessful candidates would be unhappy.
"This is an emotional journey so I think anyone who runs and then doesn't win, it's entirely natural for them to feel a low period afterward. And we've had that conversation in our caucus about making sure people are aware they may well feel that way."
Former MP Kevin Hague left Parliament in 2016 after Shaw won the last leadership contest in 2015. In 2009 former MP Sue Bradford also left Parliament after she was beaten by Turei, pointing to the defeat as one reason.
The co-leader is elected by about 150 delegates from the local branches of the Green Party which must allow members to have a say on the decision. The largest branches had a maximum of four delegates, giving an advantage to branches with the most members.
Shaw said all candidates would be told it had to be a "clean campaign" although they would not have to sign a code of conduct, something Labour Party leadership contenders have done in the past.
Shaw said there was a risk of ructions in the party but a clean campaign would help prevent that.
He said just as in a general election there was a chance members would say things that were not helpful.
"Our job as leaders of the party is to make sure if any of that behaviour does occur that we call them on it and say 'that is not the standard we want for this campaign."
TIMELINE for election:
Friday February 2 – Nominations open for all female members. Candidates can speak publicly after nomination is lodged.
Friday February 9 – Nominations close. Full list released on February 12.
Sunday March 25: Delegates grill candidates via video conference.
Monday March 26: Campaign ends, delegate voting begins.
April 7: Ballot closes.
April 8: Winner announced.
