Which modules should I look for?
When I hear you ask for a module, I think of an Arduino "Shield" but you dont need one of these. You can connect what you need directly to the board, but it will be easier if you use a breadboard.
There is a really good paper here that describes the measurement process and even shows the low-pass amplifier they used to read from the pressure sensor. You can place only the sensor inside the inflated portion and have the rest outside, or you can use a full module that is placed inside the chamber.
You will also need an air pump to inflate, and a solenoid valve to deflate. Both the pump and solenoid use 12V, so you will need a set of relays. Make sure that you have a way to restrict the airflow out, so that it deflates slow enough to get precise measurements.
Government regulation of healthcare devices raises the entry cost to market for such devices, so it's no surprise none was found in my web search.
However, there's a non-Arduino Bluetooth blood pressure cuff which logs data to iOS and Android devices