The warning was delivered by the Indonesian Foreign Ministry's Director General of Asia-Pacific and African Affairs, Desra Percaya, at this week's MSG leaders summit.
The summit was hosted by Papua New Guinea's prime minister Peter O'Neill in Port Moresby.
It was attended by leaders and officials from the other four full MSG members: Vanuatu, Solomon Islands, Fiji and New Caledonia's FLNKS Kanaks Movement.
Indonesia, which is an associate member, was represented by Mr Percaya who endorsed the MSG's plan on regional co-operation and common prosperity.
Antara reported that he warned the other states not to meddle in other countries' sovereign matters.
This came amid the MSG's ongoing deliberations on whether to admit the United Liberation Movement for West Papua as a full member.
The Liberation Movement currently has observer status.
"We remind member states (of their obligation) to continue to implement the mandate in accordance with the principles of forming MSG, including refraining from meddling in other countries` businesses much less than their sovereignty," Mr Percaya said in a press statement.
Indonesia's inclusion in the MSG in 2012 was controversial, seen by many critics as solely an attempt to quell support for West Papuan independence aims.
But Jakarta argues that with eleven million Melanesians across five of its provinces, Indonesia has the biggest Melanesian population in the world and is an important part of the region.
Leaders of the five full MSG members have been divided over whether to grant the West Papuans full membership. Yet they mostly agree on the need to remain engaged with Jakarta on their ongoing concerns about human rights abuses and the lingering self-determination issue in Papua.
Meanwhile, the Moresby summit resulted in the MSG leaders endorsing new guidelines on membership criteria.
They also referred the Liberation Movement's application for full membership to the MSG secretariat for processing.
Photo Meriba Tulo/Twitter. Caption: Melanesian Spearhead Group meeting in Port Moresby