The original picture, taken by a photographer for Norway's VG newspaper during an official visit to Lofoten, shows Solberg pouring a cup of coffee for the local politician Jonny Finstad, who seems amused by the attention.
Reddit users have used the photo to put Solberg in Star Wars, Jurassic Park, and Game of Thrones, among other scenarios.
“Hehe, I made a joke and told the Prime Minister that she was supposed to drink the cup she was pouring me - the messy one. That Erna's laughter would become an on-line hit with me in it is surprising and fun:-).” he wrote on his Facebook page, according to the local Lofotsposten newspaper.
Solberg is taking the attention in her stride.
“I realise that with the facial expression I have there, it can be tempting to use the picture in other contexts,” Solberg told VGTV in a comment.
The most upvoted picture shows Solberg pouring the cup for Ned Stark in a scene from “Game of Thrones”.
Recent photoshop battles on Reddit have featured Elizabeth, Queen of England, US presidential hopeful Donald Trump and Kate Perry.