A hydropower plant was built adjacent to the weir in 2016, which led to the sudden failure of its sluices.
The resulting survey found indications of instability and scour - when water erodes the sediments that surround the base or support structures.
They added: "The project is intended to re-establish the structural stability of the weir in order to provide continued water supply for the hydro power plant and protect the riverbed immediately downstream of the weir to prevent scour.
"This intervention is of crucial importance in order to safeguard the structure in the long term as structural failure is a potential imminent risk."
A weir is a small barrier, or small-scale dam, built across a stream or river to raise the water level slightly on the upstream side. They allow water to pool behind them, while allowing water to flow steadily over the top.
Kirkthorpe weir acts to maintain levels in Stanley Ferry cut, upstream of Birkwood Lock and back up the river to Fall Ings Lock in Wakefield.
Experts say the solution to fix the weir is to install a sheet pile cut-off at the downstream toe of the weir with a concrete infill and drainage between the piles and the weir.
They also propose installing rip rap - a layer of large stones - acting as scour protection just downstream of the new piles.
The plans were submitted in March and decision by Wakefield Council's planning department is expected soon, with the Canal & River Trust hoping to begin the work this month.
The river is typically at low flow during the summer months, with aims for the work to be completed by September.
The existing weir and its sluices were constructed in 1827 and granted Grade-II-listed status in 1986.
The structure is part-owned by the Canal and River Trust and Wakefield Council.
The site comprises a stepped and curved stone weir with three sluices positioned across the River Calder.
In 2015 Wakefield Council granted permission to Yorkshire Hydropwer Limited to build and operate a new low-head hydropower station adjacent to the weir.
The hydropower scheme utilises the flow of the river to power a single 500kW axial turbine to generate approximately 2.3 million units of electricity per year.
It was during its construction in September 2016, that it was noted that the central sluice pier on the weir had shifted, subsiding into a scour hole that had formed rapidly within the riverbed beneath it.
Remedial work was carried out to brace the structure.