Šćepović started his professional career at OFK Beograd in 2007. In 2010, he left on loan to Sampdoria. As part of the agreement, Sampdoria have an option to sign him permanently at the end of the season. At the end of the season, Šćepović was linked to Juventus and Belgian Club Brugge, signing with the latter.
Club Brugge
In July 2010 Šćepović joined Belgian club Club Brugge. After suffering a goal drought in the first half of the season, he was loaned to Kortrijk in January 2011. Belgian media also described that he was most remembered in Brugge for accidentally locking himself in a bathroom in Affligem hours before a friendly.
In July 2013, Šćepović signed a three-year loan deal with Sporting de Gijón, with a buyout clause. In September he became the first player in the history of the club who managed to score in his first five consecutive games. This great performance was rewarded with the Segunda División Player of Month prize. In January 2014 Šćepović was voted by the readers of Spanish sports newspaper Marca, best player of the first half of season, being referred as "the king ofSegunda". Also, he was named in the campaign's midway best eleven, chosen by LFP. On 6 February 2014 Šćepović was bought by Sporting outright for a €1 million fee, signing a contract until 2018. He scored 22 goals in 39 appearances for the club.
Celtic
On 2 September 2014, Šćepović signed a four-year deal with Celtic for £2.3 million, having turned down a move the day before. Eleven days later, he made his debut as a starter in a 2-1 victory against Aberdeen at Celtic Park. On 23 October, he scored his first goal for the club against Astra Giurgiu in the UEFA Europa League, scoring a header from an Anthony Stokes free kick in a 2-1 home win. Three days later, he netted his second goal for the club and his first in the league, in a 2–0 victory over Kilmarnock. The other goal of that game was a free kick from John Guidetti, earned after Manuel Pascali was sent off for a professional foul on Šćepović. On 15 March 2015, Šćepović was an unused substitute as Celtic won the Scottish League Cup with a 2–0 win over Dundee United in the final at Hampden Park, with Stokes and Leigh Griffiths starting and Guidetti as a substitute. On 24 May, he scored in each half as Celtic concluded their fourth consecutive league-winning season with a 5–0 home win over Inverness Caledonian Thistle.
On 31 August 2015, Šćepović joined Spanish club Getafe on a season long loan. Scepovic scored his first goal for Getafe a diving header in the 1–0 win over Málaga. On 28 June 2016, after suffering relegation, Šćepović signed a permanent contract with Geta. He helped the club in their immediate return to the top tier, notably scoring a brace against RCD Mallorca on 10 June 2017.
Sporting Gijón (loan)
On 12 July 2017 Šćepović returned to Sporting, after agreeing to a one-year loan deal. However, on 31 January 2018 and scoring four goals in 16 games played, Getafe and Sporting agreed to terminate the loan and was transferred to Hungarian club Videoton.
