Hello:

Yes, unfortunately if part of a tree or plant is encroaching from your yard to a neighbors, and interfering with the use of their property they can require you to remove the roots from their property. They could obtain a court order, called a mandatory injunction, requiring you to do this or to compensate them for any ongoing interference with their property. This type of interference with property rights is known called a nuisance action.

There may also be municipal bylaws in effect that deal with this issue. These differ from city o city but are usually available online. Often such bylaws can allow the city to order a to remove roots after a complaint by the property owner and if this is not done the city can do the work and then include the bill for doing so on the next property tax assessment for the neighbour that did not comply with the order.