Justice Minister Charlie Flanagan said he was ‘appalled’. Photo: Mark Condren
It is understood Mr Kenny and his family were left very shaken by the incident.
Last week, Mr Kenny spoke out in the Dáil against "fearmongering" about asylum seekers and the spread of "hatred" online and people who "peddle far-right ideology".
He has been supportive of a proposal for asylum seekers to be accommodated in Ballinamore. There have been protests against the plans.
Mr Kenny told Ocean FM Radio last Friday that he had received "sinister communications" adding it "includes death threats in them, and threats to my family".
He said it was his job to "make a stand for people's rights" and added: "I will not be intimidated."
Neighbours of Mr Kenny last night voiced their outrage at the incident.
One man, who did not want to be named, said the arson attack was completely out of line.
He added: "Martin is very respected in this community, but his support of the asylum centre has caused of lot of controversy.
"But no matter what your opinions are on this issue, you don't take it out on another man's home."
Sinn Féin leader Mary Lou McDonald condemned the suspected arson attack at the home of Mr Kenny, her party's justice spokesman.
Ms McDonald said the car was set alight at around 2.30am yesterday in "what appears to have been a very deliberate and targeted attack".
"Thankfully, no member of the Kenny family was injured, but it could easily have been different," Ms McDonald said.
She added: "An attack on the home or property of an elected public representative is a deeply serious and sinister development.
"It represents an attack on the democratic system itself."
Taoiseach Leo Varadkar also condemned the incident.
"In a democracy, there is no excuse for violence or vandalism to pursue political aims. Ever," he said, adding: "It is an attack on democracy itself."
In the post on Twitter, he said: "I totally condemn this act", as he appealed for anyone with information to contact gardaí.
Justice Minister Charlie Flanagan said: "I am appalled by the attack on Deputy Kenny's vehicle.
"In a democracy, we deliberate and debate - there is no place for violence.
"An attack on an elected member is an attack on all of society.
"It is an attack on democracy. I am asking anyone with information to please contact the gardaí," he added.
Fianna Fáil leader Micheál Martin called the incident "sinister and shocking".
He said it was "an assault on our parliamentary democracy and those responsible must be brought to justice".
A Garda spokesperson said yesterday: "Gardaí in Mohill, Co Leitrim, are investigating an incident of criminal damage by fire which occurred in the Aughavas area of Co Leitrim at approximately 2.30am this morning, Monday 28 October 2019.
"A car was discovered on fire at this location.
"Gardaí and fire personnel attended the scene. The fire was contained to the car.
"No other property was damaged and no injuries were reported.
"A Garda forensic technical examination will now take place."