Ward impressed on his first international start as Gareth Bale and Hal Robson-Kanu secured a valuable three points, but Hennessey hopes to return against England.
"I had one [a spasm] and missed the Liverpool game at home for Crystal Palace [in the Premier League last season]," he said.
"I had a similar one [before the Slovakia game]. So I'll have an injection and will probably be back in 24 hours which sounds crazy.
"It is one of those things that you go from broke to mended in about 24 hours. It was an unsettling time for myself, but one motto is 'Together Stronger' and it is all about the boys.
"I thought Danny did really well, it was a big situation for him to come in but I thought he was tremendous."