Tom Pursglove welcomed the additional funding for Care after Combat, which was co-founded by comedian and TV presenter Jim Davidson in 2015.
The charity is only currently able to reach one in 10 prisoner veterans and needs urgent funding to roll out its services UK-wide and support all eligible veterans currently serving sentences.
Mr Pursglove said: "The Armed Forces Covenant is an agreement between our country and those who put their lives on the line to defend it, and we have a responsibility to look after the welfare of all our veterans, especially as they leave the Armed Forces and make the massive and often daunting challenge of transitioning to civilian life.
"Having been a longstanding supporter of the charity, I know that Care after Combat provides dedicated support for those least able to make this transition and who often fall into the prison system as a result.
"We must do everything we can to end this vicious cycle - I welcome the additional funding announced at the Budget for the Armed Forces Covenant Fund and I am pleased to pledge my ongoing support."
It is estimated that there are currently 3,500 former servicemen behind bars in England and Wales.
According to Care after Combat, this represents the largest single occupational cohort within prisons – and one of the most vulnerable groups.
The charity mentors incarcerated veterans serving the final 18 months of their sentence to help them make the successful transition from prison life, back into the civilian population.
Over the past three years, it has expanded its scope to provide services for more than 300 incarcerated veterans in almost 30 prisons, helping to reduce first-year re-offending rates among service users to only eight per cent.
This is compared to the 45 per cent first-year re-offending rate among the wider prisoner population.
Mr Davidson, the chief executive officer of Care after Combat, said: "At a time when our prison service is struggling to cope, Care after Combat could play a greater role to reduce re-offending and help former veterans by restoring the sense of stability and purpose which they enjoyed whilst serving in the Armed Forces.
"While we welcome the additional Â£10 million cash injection to the Armed Forces Covenant Fund to support mental health projects, we call on Government to recognise the specific requirements of this group and increase funding for veteran prisoner community transition services.”