The landmark business fears plans to double the size of Buchanan Galleries will choke roads around the city's main square.
Mall bosses have lodged plans for a new 1700-space car park near the square as part of their £300 million expansion, supported by £80m in controversial Tax Incremental Funding (TIF) from Glasgow City Council.
The new car park, for the expanded centre, will have 1300 fewer spaces than the existing car park.
The planned car park will have one exit, rather than the existing two, and will also be closer to George Square
Hotel bosses worry the new multi-storey car park, to the east of Queen Street station and exiting on to North Hanover Street, will cause congestion at its George Square site.
A hotel executive, in a formal objection to planning permission seen by the Evening Times, said: "This could have a negative impact on the surrounding roads and the flow of traffic around the George Square entrance to the hotel."
Other city centre businesses, notably the rival St Enoch Centre, have been long-standing opponents of the TIF, which it believes amounts to unfair state support of one business against another.
Millennium's objections come after Strathclyde Partnership for Transport put a holding objection on the expansion of Buchanan Galleries, expressing concerns over several elements, including the effect of the new car park on key bus routes.
Buchanan Partnership, the joint venture which owns the mall, has said it believes the expansion will improve transport in Glasgow.
Glasgow City Council is in the unusual position of both judging the planning application from Buchanan Partnership while supporting the TIF scheme.