The image of Bennett holding the large bag of cannabis was taken during a research trip to Canada. The second image, of the MP holding a bag of 14g of cannabis, was taken in Parliament, where she held the bag to show how much New Zealanders would be able to purchase.
Sanjay Patel, who created the meme, captioned it : "S**t, she went through it quite quickly".
"Well, actually, I've got to say I have an example of the kind of amounts that are in other countries," Peters said, holding up the meme.
"In this case, it's very hard to tell the difference between the dope and weed," he added.
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"Ms Bennett is a world-class expert on that and I do defer to her knowledge and experience."
"If the minister would like a picture of me for his wall he can just let me know," Bennett replied.
"On the question of the picture on the wall, it's very hard to get a photograph when you're spending all your time - as that member does - in front of a full-length mirror," Peters replied.
Parliament erupted in laughter after the exchange.