Rossums' Instagram has more than 1.6 million followers and almost 3000 posts.
One of the photos Rossum posted was of her at Lake Tarawera.
The stunning views prompted the actress to say New Zealand "looks like CGI".
The actress arrived in New Zealand on Christmas Eve, beginning her travels in the South Island.
When contacted by the Rotorua Daily Post Solitaire Lodge would not say whether or not she was staying there.
Rossum is most well known for her portrayal of Fiona Gallagher in the hit series Shameless.
She starred in the science-fiction film The Day After Tomorrow (2004) and received critical acclaim for her performance in the leading role of Christine Daae in The Phantom of the Opera in 2004.
She is travelling with her fiance, Mr Robot creator Sam Esmail.