Vutov made his senior debut for Levski on 8 April 2012, in a 1–1 league draw against Lokomotiv Sofia at the age of 15 years and 307 days, making him the youngest player ever to have played for the club.

During the winter break club's boss Todor Batkov announced that Levski are going to sell Antonio to Italian side Udinese.

[7] Vutov made his Udinese first-team debut on 18 February, in a 0–3 friendly loss against Hajduk Split at Stadion Poljud, playing 78 minutes.

On 30 July he debuted with the giallorossi and scored his first official goal for the club in a 2-1 win against Alto Vicentino in a Coppa Italia match.

[11] On 26 April Vutov scored a header after a magnificent assist provided by Todor Nedelev in the 1-1 draw with FC Vereya Stara Zagora during the 2nd leg of the semi-finals for the Bulgarian Cup.

[13] On 24 May Vutov scored the second goal for the 2-1 victory over Ludogorets Razgrad helping Botev Plovdiv to win the Bulgarian Cup for the third time in the history of the club.

[17] He made his debut for Bulgaria national football team on 31 March 2021 in a World Cup qualifier against Northern Ireland.