A registered nurse, who has experience working in ICU wards, Varnhagen has become the first known AFL or AFLW player to refuse the COVID-19 vaccination.
The Crows have issued a statement following multiple reports but stressed they could not confirm or deny any player's vaccination status due to medical confidentiality.
"Our club strongly encourages people to be vaccinated against COVID-19," a club statement read.
"The club remains committed to following the health advice and guidelines set by government and the AFL."
The AFL is yet to finalise a vaccination policy but the Victorian government's requirement about a range of workers, which includes footballers, needing to be vaccinated came into effect last Friday.
Most Victorian clubs have confirmed to AAP that their AFLW programs are all compliant with the government vaccine protocols and players have been cleared to train and play.
There is no similar vaccine requirement in South Australia but the state's healthcare workers do need to have at least one jab before November 1.
Varnhagen, who played in the Crows' 2017 and 2019 premierships, posted a video on social media on Saturday showing people marching in Adelaide for "freedom of choice".
The 28-year-old then followed it up with another clip holding a sign that read "health care hero's (sic) in 2020 ... unvaxed unwanted in 2021".
Varnhagen has played 31 games for the Crows across the first five seasons of AFLW.
The AFLW season is due to get underway on January 6.
AAP with The Project