Katrine Veje

In 2007, Veje was awarded the Danish Football Association's prize for Young Player of the Year.

Seattle Reign

In January 2015, it was announced that Veje had signed with Seattle Reign FC for the third season of the National Women's Soccer League in the United States. Of her signing, Reign FC head coach Laura Harvey said, "I have had my eye on Katrine for many years, having first seen her when I was an assistant coach with the U17 England squad...We believe she is capable of bringing something special to our club and to the NWSL." She made her first appearance for Seattle on 12 July 2015 against Portland.

Brøndby IF

In October 2015, Veje decided to return to Brøndby IF. With Brøndby IF, she won the Danish league and cup in 2017.

Montpellier HSC

In June 2017, it was announced that Veje had signed a two-year contract with the Division 1 Féminine runners-up Montpellier HSC.

Arsenal

In January 2019, it was announced that Veje had signed a contract with Arsenal.

Everton

On 19 July 2024, it was announced that Veje had left Everton.

Crystal Palace

On 1 August 2024, it was announced that Veje had signed a contract with Crystal Palace. On 10 June 2025, it was announced that Veje was departing the club upon the end of the 2024–25 season, having made a total of 20 competitive appearances for Palace.

Veje debuted on the Danish national team in a friendly against England in 2009. She was named to national coach Kenneth Heiner-Møller's Denmark squad for UEFA Women's Euro 2013 as well as to Nils Nielsen's UEFA Women's Euro 2017 squad.

LdB FC Malmö (now FC Rosengård) Damallsvenskan: 2011, 2013 Swedish Super Cup: 2011, 2012 Seattle Reign FC NWSL Shield: 2015 Brøndby IF Danish League: 2015, 2017 Danish Women's Cup: 2015, 2017 Arsenal FA Women's Super League: 2018–19 Women's League Cup: 218–19 FC Rosengård Damallsvenskan: 2021 Swedish Cup: 2021–22 (did not play in final)