The firm plans to redevelop the area, most likely for housing and leisure facilities.
Miss Tolhurst, whose constituency covers the dock, says she is deeply disappointed by the move.
The Rochester and Strood MP said: "I know this news would have sparked a lot of anxiety for everyone who works there.
"Chatham has been an important commercial port for centuries, and the site is a vital local and national asset that deserves protection now and for future generations.
"There is now a real threat to its long-term future because of Peel L&P's desire to redevelop the site.
"The docks are situated in an area which provides great economic development in the Medway Towns, delivering employment and a sustainable location for industrial activities."
However, Peel says the estate is "financially unsustainable" as a port and has put it forward as a potential place for housing, retail, tourism and leisure to be considered in the upcoming Medway Local Plan, which covers future developments in the Towns.
The landowner is planning to offer "alternative locations" to docks-based businesses, which could see firms move to Sheerness - a port it also owns.
Miss Tolhurst added: "Over the past few months, I have been attempting to meet with Peel to discuss a number of concerns that I have for the River Medway, including their plans to develop the site.
"Unfortunately, they have failed to commit to meeting, I have made representations about my concerns, and those of local businesses to the Minister for Maritime and Shipping, and I will continue to press Peel and stand up for the interests of all those that work at the docks.
"I am totally against these plans, and will be strongly objecting to Medway Council’s planning team today."
Dave Harris, who leads on planning at the local authority, has also responded to the plans.
He said: “It is a landowner’s decision as to whether existing use of a site continues and the local authority has no control over this.
"If the landowner would like to change the use or develop the site, they would require planning permission; they need to submit a planning application to the council for consideration.
"Any such application will be carefully considered against national and local planning policy.
"We have not currently received any plans for this site.”
Miss Tolhurst is urging any employees or local constituents who are concerned about the future of Chatham Docks, to contact her office.
She added: "I will do everything I can to help and support you at this worrying time."