The boar, thought to have escaped with her piglets from Drumlean Estates, Stirling, has been spotted around the primary school in the village of Aberfoyle and locals fear children could be injured.
Residents have raised concerns about the boar being on the loose. Some say they have seen them act in an "aggressive manner".
Stirling MSP Bruce Crawford said: "Concerns have been expressed to me about the potential danger the wild boar poses to the community. With the close proximity of the Aberfoyle Primary School and the combative nature of the wild boar sow, members of the public could be injured.
"I have referred this matter to Stirling Council and Scottish Natural Heritage to ascertain what responsibilities they have dealing with the situation given the regulatory requirements and to seek their advice on how to this situation can be resolved.
"Given wild boars' reputed talent for rapid reproduction, early action on this matter would presumably be preferable."
A Scottish Natural Heritage (SNH) spokesman said that the organisation was working with the police and Stirling Council to agree a "suitable course of action" to deal with the escaped sow and its piglets.
He said: "We are examining practical measures to deal with the animals that have escaped.
"The owners of the animals are responsible for keeping them in an enclosure, and the police have been informed of their failure to do so. We cannot expect the owners to take action to recover the animals, however, as they are now not on their land. That's why we are working with others to agree the most suitable course of action.
"In terms of impact, there is the potential for the feral pigs/ wild boar to increase grazing and trampling pressures on fragile habitat, which is why we are keen to remove them from the area."
SNH is currently finalising work for the Scottish Government recommendations on the issue of wild boar/feral pigs in Scotland.
The spokesman added: "This is in the wider context that we are aware of existing wild populations and that eradication of them is extremely difficult."
Stirling Council said it had been informed about the boar being on the loose and would take steps to ensure children are kept safe if they are deemed to be in danger.
A council spokesman said: "The safety and well-being of the children is our main priority.
"In any situation where there may be risk, we would work with partners to make sure that all appropriate measures were in place."
No-one from the Estate was available for comment.