The services will stop at exactly 1506 BST on 15 April for two minutes to remember those who died.
At Sheffield Wednesday's stadium, 96 Liverpool fans were crushed to death when the club took on Nottingham Forest in an FA Cup semi-final in 1989.
Merseytravel said the silence will show that "the victims of the tragedy are not forgotten 20 years on".
In addition, the Mersey Ferries will moor at the Pier Head and all vehicles will stop in the Mersey Tunnels, when safe to do so, to observe the two minute silence.
Greater Manchester is also arranging for buses at depots in Wigan to observe the silent tribute for what is considered to be one of Britain's worst sporting disasters.
'Not forgotten'
Neil Scales, Merseytravel chief executive, said: "This is our chance to pay tribute to those who lost their lives at Hillsborough and for the families that survive them.
"We hope people travelling by whatever mode of transport appreciate this gesture; it is two minutes in a lifetime and a silent tribute to show that all of the victims of the tragedy are not forgotten 20 years on."
The plan comes just days after Merseyside musicians released a record to mark the 20th anniversary of the Hillsborough football disaster.
The single, called the "Fields of Anfield Road", was launched at music venue The Picket on 26 March. Past and present Liverpool FC players and families of the victims attended.