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.
As long as the pipe intake is higher than the stream bed, it cannot drain it dry.
The bottom is sized to maintain a minimum safe flow rate for the stream ecology.
The middle is sized for the maximum flow rate of your application. A dry pipe signals that the stream ecology is in danger.
The top is for overflow when your intake pipe is full.