Elected police and crime commissioners were introduced in 2012 with the aim of improving accountability and creating a link between police forces and the communities they serve.
However, Jones said the model had “failed to live up to expectations” with only 16% of voters able to name their local PCC.
In Wales, just 17% of voters took part in last year’s PCC elections.
Policing and justice in Wales and England is the responsibility of ministers in Westminster.
Jones explained that the functions of PCCs in England would be transferred to elected mayors “wherever possible”.
With no elected mayors in Wales, Jones said the UK government would “work with the Welsh government…recognising the unique nature of Welsh arrangements”.
Responding to her statement in the Commons, Plaid Cymru MP for Caerfyrddin Ann Davies said the announcement “makes clear the absurd complexity of an England and Wales justice system”.
“The UK government will look to the Welsh government to help replace the PCC system in Wales, but has refused the same government powers over policing.”
She asked the minister if she agreed that “devolving the entire justice system to Wales makes the logical sense”.
Jones replied: “This announcement, just to be clear, isn’t about the devolution of policing – it’s about the structural changes to a model that simply wasn’t working.”
The debate over whether responsibility for policing and justice should be transferred from Westminster to Cardiff is long-running, including within Labour.
At odds with party colleagues in London, Welsh Labour would like to see the powers devolved.
“Our position in Welsh Labour is clear on this,” the First Minister Eluned Morgan said on Thursday.
“We’ll be having conversations with the UK government on the future of policing.”
Welsh Secretary Jo Stevens accepted that the debate “may rumble on”.
