The Wales global was seen holding one hand in the air and the other above his mouth in a social media post on Sunday.
The goalkeeper has his right arm outstretched, while his left hand is across his upper lip.More news: Athletics Expect Heisman Winner Kyler Murray To Enter NFL Draft
The Wales worldwide, however, immediately denied making a Nazi salute, explaining it was simply a case of poor timing.
"Yesterday evening I had a meal with my team mates and we had a group photograph", Hennessey wrote on Twitter.
He goes on to say that he waved and shouted on the person who had been clicking the picture to get on with this and at the same time, he had put his hands over his mount for carrying the sound. It is later that it had been brought to his attention that the posture in the picture appears like he is making an inappropriate kind of salute. "Love and peace Wayne".
Palace boss Roy Hodgson recalled Hennessey to the starting line-up for the third-round tie against Grimsby at the weekend.More news: England rugby chief Simon Kemp makes 'significant changes' revelation after injury rise
Hennessey, who has made 81 appearances for Wales and helped his country to the Euro 2016 semi-finals, played in the victory.
Palace are 14th in the Premier League, six points clear of the relegation zone.
The Eagles host Watford on January 12 at 10 a.m. ET.More news: Disappointed about Alien Blackout? An Alien MMO is in the works