In 1971 at the internet's infancy, there was a network called ARPANET operating at Standford and MIT. Small packets of text could be sent from one terminal to another, so some resident students ordered Cannabis by sending a message asking where to meet and how much money to bring. The money exchanged was done in person, so this wasn't the first payment sent through the internet, but the overall transaction was comparable to a modern meetup arranged on Craigslist or Kijiji.
The first cash payment sent through the internet only happened in 1994 to a Pizza Hut in New Hampshire on a localized network called NetMarket, although there is some controversy as CDconnection has made the claim they've been selling Music CD's since 1990 on their official site using NetMarket aswell.
These are the first documented transactions of their time, but it's very likely there were undocumented transactions within foreign countries that predate western internet as we know it. In 1984, there was a secret network which piggybacked ham radios which covered the entire USA coast to coast, but it wasn't reliable and an email would take a week to travel across the country in the best conditions.
The internet has always been a place where shady things go down, and it doesn't come as a surprise that weed is the first transaction made using it. People think the sales of drugs using the internet is a new concept, but its the first thing to ever be ordered on the internet.
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