Erasmus controversially used the role to pass on advice to his team during the British and Irish Lions' series and autumn Tests last year.
"The number of people who aren't players interrupting the flow of the game was getting out of hand," said World Rugby's Mark Harrington.
Head coaches and directors of rugby are explicitly banned from carrying water.
The new rules also state that water carriers will be allowed to come on to the pitch only twice in each half. At other times they must remain in a technical zone on the touchline.
Water will be available for players behind the dead ball line or from their teams' technical zone if they need to rehydrate outside the agreed windows.
Penalties could be awarded against teams if their off-field staff infringe the new trial laws that come into force globally from 1 July.
"No-one should approach, address or aim comments at the match officials, save for medics in respect of treatment of a player," states one.
"Should this happen, the sanction will be a penalty kick."
Erasmus is serving a ban from any involvement in Springboks matchdays as punishment for an hour-long video he made criticising the officials' performance in the first Test defeat by the Lions in July, a series the home side went on to win 2-1.
The new rules have been introduced following feedback from around the world and are supported by players' union International Rugby Players.