The 250-word email contained three links to Parliament's website where people can make a submission on the bill.
"Submissions close next Friday. Don't miss your opportunity to have your say on this important reform," read one link.
While it is not unprecedented for political parties to ask supporters to submit on legislation, it is fairly uncommon.
Watts said the email showed Labour was worried about a likely avalanche of submissions against the proposals. A group opposing the reforms has signed up 31 of the 67 councils affected. Auckland Mayor Phil Goff is also opposed.
"When you're having to ask your own supporters to make a submission on legislation it shows how desperate the situation has become," Watts said.
"We know there is overwhelming opposition to reforms across the country."
After a select committee hears submissions on a bill, it will publish a report on what it has heard, including any recommendations it wishes to make.
Those reports will often include a breakdown of the number of submissions that were for or against the bill. It might be damaging for Labour's mandate to pass Three Waters legislation if an overwhelming number of submissions were against the bill.
Labour plans to take the management of freshwater, wastewater and stormwater - the three waters - out of councils' hands and into one of four enormous water entities.
Councils will nominally own a share of the entities, but will in practice have very little say over how they are run. The entities will be governed by boards which are ultimately appointed jointly by council representatives and Māori - a co-governance proposal that has proved controversial.
Local Government Minister Nanaia Mahuta's office referred a request for comment to Labour's campaign team. Labour is yet to respond to a request for comment.