Heath Hayes & Wimblebury Parish Councillor Philippa Haden launched a petition to have the sign outside the McArthurGlen outlet in Cannock taken down.
More than 130 residents have put their names to the petition since it was launched on Thursday, with more airing their concerns on social media.
Councillor Haden said: "Residents of Hawks Green have been very patient and have had to put up with severe traffic issues, overnight building works and general disruption, but this huge sign has upset them because it is a permanent structure, not in keeping with the area.
"The centre itself, has an attractive frontage, residents have posted pictures on social media showing how it towers above their houses and dominates the landscape and is so unnecessary.
"To go to work and then to come back and see a very large sign in your back garden, it's very upsetting.
"It's not in keeping with the development, it's been quite sympathetic, it looks like a little village, it's quite pretty to look at, but now they've put up a massive blue sign, it's ginormous.
"Signs are already on islands approaching it and it's not something you pop along to, you plan to go there, plus sat navs are brilliant."
The petition is supported by District councillors Adrienne Fitzgerald and Phil Hewitt and will be presented to McArthurGlen and Cannock District Council.
Local residents were also upset when the shopping village was named McArthurGlen Designer Outlet West Midlands, with the name referencing the West Midlands but not Cannock or Staffordshire.
Work has been ongoing at the site since July 2018 and major changes have been made to the nearby road system.
When it opens the shopping village will feature around 80 brands, restaurants, cafes, and 1,400 car parking spaces.
The opening was delayed from the original date of Autumn 2020 in July because of the impact of coronavirus.
On the petition's website Councillor Haden says: "The sign at the McArthurGlen Designer Outlet has been erected and is a monstrosity.
"The aim of the shopping village was to blend into the area and nature. This does not do this!"
About 1,000 retail jobs are expected to be created when the site opens in early 2021.
To view the petition, visit change.org/p/cannock-chase-council-remove-the-mcarthur-glen-sign
Mike Thomas, centre manager for McArthurGlen Designer Outlet West Midlands, said: “We would like to reassure local residents that the totem signage at West Midlands Designer Outlet is a fully permitted part of our development and a feature of McArthurGlen centres around the world.
“Its installation marks an exciting milestone as we move ever closer to bringing our collection of iconic brands and significant job opportunities to the local community in what will be one of the UK’s major landmark retail destinations.”