Question: I am trying to design a pipe which takes water from a river and transports it to a reservoir.

However, I do not want my pipe to take all of the water from stream, because that will create all sorts of environmental problems.

How do I make sure that this does not happen?

The flow rate in the stream is $0.02 m^{3}/s$ and the stream is $1m$ wide and $1.25m$ deep. 

Do I just need to make sure that the flow rate in my pipe is not greater than $0.02 m^{3}/s$?

Answer: 
You can put a valve on your pipe to control the flow.

Or partition the stream by means of a short concrete wall which looks like an indented grout trowel upside-down . Say two opening for the stream and one leading to a small pond downstream feeding your pipe.
Some countries have Water or River authorities that decide how much water you can have from the stream and in certain seasons that can be zero...

So, intakes are designed to trap debris, both floating and sediment, a coanda screen is a good option for this. Then the intake is also designed so that if there is insufficient volume in the stream then your supply stops, this can be achieved by a simple dam for example.