Hendrick's 2016–17 season did not get off to a good start as he picked up a hamstring injury in a 2–0 loss to Barnsley on 13 August 2016.
On 31 August 2016, Hendrick joined Premier League side Burnley for a club record £10.5 million fee on a three-year deal. He made his debut on 10 September, coming on as a 75th-minute substitute in a 1–1 draw at home to Hull City. He made his first start for Burnley on 17 September, playing the full 90 minutes in a 3–0 away defeat against reigning Premier League champions Leicester City. Nine days later, Hendrick netted his first goal for Burnley in a 2–0 home win over Watford with a header from a Steven Defour cross.
He scored his second goal for his new club on 10 December 2016 with a 25-yard volley in a 3–2 home victory over Bournemouth. Hendrick's strike was nominated for Goal of the Month; it came third in the public vote, behind strikes by Alexis Sánchez in second and Henrikh Mkhitaryan in first and would later earn him the Burnley Goal of the Season award. On 4 February 2017, he was sent off against Watford in the sixth minute for a two-footed challenge on José Holebas as Burnley were defeated 2–1 at Vicarage Road.
Hendrick scored his first goal for Ireland on 5 September 2016. He opened the scoring in the third minute in the 2–2 away draw against Serbia in a 2018 World Cup qualifying match with a low shot just outside the penalty area which was deflected in off Branislav Ivanović.