Police were alerted after water bailiffs from the River Tweed Commission found the trap within the river at Horncliffe on Monday, June 28.
As well as the otters, the net also contained 13 dead sea trout and a dead cormorant.
It is believed the net had been in place for up to two weeks.
Otters are a protected species under European law and along with cormorants, are protected in Britain under the Wildlife and Countryside Act 1981.
Salmon and sea trout are protected under the Salmon and Freshwater Fisheries Consolidation (Scotland) Act.
Police are now appealing for anyone with information that can help trace those responsible for the poaching net to come forward immediately.
PC Ruaraidh Hamilton, wildlife co-ordination officer, said: "This sort of tragic incident displays the reckless nature of poachers who put nets across rivers.
"Otter numbers went into rapid decline during the 50's through to the 70s and as such are protected under European legislation.
"They feed on the fish within the river and would have been attracted to the dead trout within the net before being caught themselves and drowning.
"Anyone with information about river poaching or who can help us locate the individuals responsible for this illegal trap is asked to contact police immediately."
Anyone with any information should contact Lothian and Borders Police on 0131 311 3131, or the charity Crimestoppers in confidence and complete anonymity on 0800 555 111.