About 14 acres of woodland has been cleared at Stanmore Industrial Estate and the Forestry Commission confirmed it was conducting inquiries into whether any laws had been broken.
In addition to a felling licence, other permissions to cut down trees may also be required before a landowner can undertake the work.
Concerns were first raised by residents of The Hobbins, who said the woodland had acted as a buffer blocking out noise and light pollution before waking up last week to see diggers on site.
The Forestry Commission said it was "aware of reports of alleged illegal felling near Bridgnorth" and that it could not comment further on active investigations.
A spokesman said: "We take the protection of trees and woodlands extremely seriously and won't hesitate to investigate any allegations of illegal tree felling.
"If there's no felling licence or other valid permission in place, or if the wrong trees are felled, we will take action."
Shropshire Council is also working to see if there has been a breach of licence and confirmed the clearance was not in relation to its ongoing local plan process.
Wildlife protection officers from West Mercia Police have also attended, but said no wildlife offences had been committed.
Resident of The Hobbins, Darren Hodson, said: "We were all shocked to see bulldozers ripping up trees by the roots last week.
"It acted as a fantastic buffer between the industrial estate and residents. Now, with such a quantity of trees having been removed, it's very alarming what residents are going to see as lockdown eases.
"We also have protected species living around the area so we're also concerned about the damage to our wildlife."
A spokesman for Stanmore Industrial Estate said they were not aware of any laws which had been broken.
They said: "We're returning the field for agricultural use.
"There are no Tree Preservation Orders on any of the trees and it is our intention to plant a screening buffer between Stanmore and The Hobbins, which is likely to be planted in the autumn."
Before anyone can cut down trees, they may need to get a felling licence from the Forestry Commission; depending on whether an exemption to the need for a licence applies.
Felling trees without the authority of a felling licence, where one was required, currently carries a penalty upon conviction in a magistrates court of £2,500, or twice the value of the timber felled. Provisions within the Environment Bill which is currently before Parliament, will increase this penalty to an unlimited fine, set at the discretion of the court.
The Forestry Commission can also serve a restocking notice upon the individual responsible for the land where unlicensed tree felling occurred, either with or without having secured a conviction. This notice compels the individual to restock the land with trees. Failure to comply with this notice will result in an Enforcement Notice being issued, which, if not complied with, may result in a separate offence being committed which carries a penalty of an unlimited fine.