Some customers had nearly two months’ worth of mail delivered this week, along with a letter of apology from An Post.
An Garda Síochána confirmed the investigation involves a member of staff in the Dublin 12 area.
An Post said that as the investigation is ongoing, they cannot provide further information on the matter.
A special phone line has also been provided for the impacted customers.
A garda statement said: “Gardaí are investigating a report of the alleged theft of a volume of material from a national service provider, involving a member of staff in the Dublin 12 area.
“An Garda Síochána is liaising with the affected service provider on the matter. Investigations are ongoing.”
A spokesperson for An Post said that, following an investigation by the company in conjunction with gardaí, several “undelivered letters and small packages” for addresses on one postal route in Crumlin had been located.
“An Post sincerely apologises to the affected customers for this upset and inconvenience, and we are working to have this mail delivered as quickly as possible,” they added.
Fianna Fáil TD for Dublin South Central, Catherine Ardagh, said it has been an “extremely stressful time” for residents in Crumlin.
“When we realised there was an issue with the postal service into Dublin 12, we raised it repeatedly with An Post,” she said.
“When we began raising it initially, we were unaware of the scale that appears now to be involved. By the end of the [election] campaign, it was being raised with me so often.
“When I posted the video online, the office phone started ringing with people contacting me saying they hadn’t received mail for weeks.
“During this time, An Post repeatedly indicated to us that they were investigating it.
“They did not provide any additional information until this week, when they issued a formal statement confirming an investigation had been launched and the gardaí were involved.
“This has been an extremely stressful time for the affected residents in Crumlin, and An Post has work to do to rebuild their reputation and trust.
“Medical appointments were missed, important documents were not received,” she added.
She also noted that most of the post is delivered “on time and without issue” and that most of her constituents receive an excellent service from An Post.
However, she said there was clearly a “very serious problem” on this postal route.
