There are three different ways you can have this set: 3 night minimum at discounted rate continuously, a package rate, or with a maximum stay setting. 

Firstly, you will need to create a new rate.
To do this you will need to go to New Rates (under the Rates heading in the iBex menu), fill out the necessary details (such as marketing name, number of guests, room assignment, etc)
Please see further instructions here on how to create a new rate:

(i) By creating the new rate, customers will be able to book for a minimum stay with the discounted rate. 
As iBex rates are calculating an average nightly rate, you will need to add a 3 night minimum to the rate, and then divide the 2 night price over the 3 nights to calculate the nightly price. 
For example, if the standard nightly rate is $100 per night x 2 nights = $200
$200 / 3 nights = $66.67 nightly.

This will appear as below on your iBex website booking screens:

(ii) If you set this up as a package rate, you can have the discounted amount as a package rate, as well as a secondary rate. 
The secondary rate will allow customers to book the standard rate if they are staying longer than 3 nights.
*Ensure you enable the Package Rate option under the Advanced Rules subheading if you would like to have a secondary rate. Please note that package rates are not supported by sales channels.
With the 3 night minimum, the package rate would be $200, and the secondary rate would be $100.

This will appear like the below on your iBex website booking screens: 

(iii) You can alternatively use the maximum stay setting, to ensure that guests aren't able to book the discounted rate for more than 3+ nights. 
This will restrict their booking with this rate for 3 nights only.
*This option is also not supported by sales channels.

This will display like the below on your iBex website booking screens: