It was "totally unacceptable" that the bill failed to rule out "testing these recreational drugs on innocent animals".
When former Associate Health Minister Peter Dunne said in the House that it was never his intention to have animals experimented on, Mr Banks said this could not be guaranteed and described Mr Dunne as a "puppy-hater".
If it passed, Ms Mathers' amendment would block drug-makers from using information gained from animal testing to prove that their products were "low-risk".
It was opposed by National and United Future.
Whether it succeeds could hinge on the fact that new Labour MP Meka Whaitiri will not be sworn in when the vote is held.
At present, the amendment is believed to be supported by 60 MPs and opposed by 60 MPs. New Zealand First has not publicly stated its position but is expected to support the amendment.
It was expected to pass if Ms Whaitiri was able to cast her vote. But the new Ikaroa-Rawhiti MP, who was elected in a byelection last week, will not be sworn in until the end of the month.
If the vote is tied, the amendment fails.
Animal rights amendment
For: Labour, Greens, Mana, Maori, Act (53 votes)
Against: National, United Future (60 votes)
Undecided: NZ First, Brendan Horan (8 votes)