There’s a post office in the connecting passage between the arrivals and departures terminal. The terminal map (PDF) literally mentions the area as “connection between terminals”. The post office is on the first floor, on the same level as Baggage Claim 1-3.
Mail drops are also listed “in front of the Departures and Arrivals Terminals.” These appear to be outside, pre-security. I found one hidden in a Google photo at the Departures terminal; see if you can find it.
Mark Lee submitted the following information about a post-security mail drop:
Airside in shopping concourse – red Posta Româna posting box with 1100 collection – on left hand side as you face towards the gates coming from Passport control.
I found a photo on Google that might be the box; it’s red, square-ish, and across from the Brioche Doree, hanging from a pillar.
Last updated 24 December 2018