Tobia Ellwood shared the initiative as he opened a debate on the Armed Forces Covenant, intended to protect veterans who have left the armed forces.
Mr Ellwood told MPs the Ministry of Defence and Ministry for Housing had signed up to a statutory duty for commanding officers to refer vulnerable individuals to councils for housing.
"This is so important," he said.
"It means we should not see people who might become homeless leaving the armed forces with nowhere to go because their plight will be flagged up."
The Minister also focused on suicide prevention, announcing a new working group had been set up to investigate how best to tackle the problem.
He said: "We have set up a new suicide prevention working group to urgently look at the cases of such distress in serving personnel.
"It will look at how to address the issues affecting those in such distress now and how to prevent others feeling the same way."
He added: "It will look at the triggers in service to ensure all future veterans have the resilience they need while serving and after they leave."
Mr Ellwood further warned that the military was not the sole cause of suicide, saying there were usually other complex underlying issues.
He said: "Suicide is the most tragic symptom usually of many other issues such as mental health or family breakdown, debt, unemployment or a myriad of other problems.
"It's inaccurate, disrespectful and trivialising to link suicide solely to military service.
"But I do say that in some cases military service plays a role and we need to better understand the causes so we can try to prevent further suicides in future."
However, he confirmed a Veterans Board had been introduced to enable ministers to "hold to account those other departments that need to upgrade their support for both veterans, veterans' families and the Armed Forces as well", including on issues of homelessness and suicide.
He added: "It is absolutely important we do not shy away, whether it is perceived or otherwise, from our responsibility to help those veterans who may feel that they have gone into a very, very dark place themselves."