Krajnc began his football career at the age of eight, when his father took him to the Slovenian club Maribor for a trial.[2] He signed his first professional contract with Maribor at the age of 16 and played for the main squad in a couple of friendly matches. On 29 May 2011, he played his first and only 1. SNL match for Maribor in the last round of the 2010–11 season,[3] with Maribor already being crowned champions. At the time of his debut, he was the youngest player ever with an appearance for Maribor in a 1. SNL match, a record which lasted until 25 March 2012 when it was surpassed by Petar Stojanović.[4]
On 3 April 2011, Krajnc signed a pre-contract with Italian Serie A club Genoa.[5] The transfer fee paid by Genoa was undisclosed, but was reported to be close to €1 million. He joined his new club on 1 July 2011[6][7] and was assigned to Genoa's youth team, which he also captained, before making his debut for the first team on 27 October 2012 at San Siro in a league match against AC Milan.[8] With 18 years, one month and 14 days, he became the youngest Slovenian player with an appearance in the Italian top division, Serie A.[7]
On 3 July 2013, he moved to Cesena in a temporary co-ownership deal.[9] In June 2015, Genoa acquired Cesena's share and became the sole owner of the player's rights.[10]
On 31 August 2016, Krajnc joined Sampdoria on a season-long loan.[11] In the second part of the 2016–17 season, he was loaned to Frosinone.[12]
On 20 June 2018, Frosinone turned Krajnc's loan into a permanent deal for an undisclosed fee.[13]
On 24 August 2021, Krajnc joined Hannover 96 on a three-year contract.[15]
On 23 August 2023, Krajnc returned to Italy and signed a two-year deal with Catanzaro.[16]
After 13 years of playing abroad, Krajnc returned to his childhood club Maribor on 7 September 2024 and signed a contract until 2026 with the option for another year.[17]
Krajnc is from Kapla na Kozjaku in the hilly region of northeastern Slovenia near the Austrian border, roughly 37 km from the city of Maribor.[2][21] Before moving to Maribor he usually had to study and do his homework on the back seat of his father's car, traveling to and from training.[2][8]