I booked a flight and was issued a travel itinerary. It contains my name, booking reference, E-ticket number and some other information.
For proof of absence, I need to forward this document to a third party (an educational institution). Is there any security risk of doing so? And is there any way to prevent/minimize the risk?
There is a risk. At a minimum, you are revealing the personal information, including your full name. The itinerary may also contain (depending on its format) your date of birth and travel document information (see What harm can be done with a copy of one's passport?). You're also revealing your whereabouts: somebody could, at least theoretically, follow you or know when you won't be home and break in.
In addition, all the information you need to change the itinerary is generally printed on the itinerary. Someone could go online or call the airline and use that information to cancel your trip or reroute you to Siberia. Getting that fixed could cost you time and money. They could engage in smaller mischief such as ordering you an unwanted vegan meal or giving you a middle seat directly in front of the lavatory.
You could minimize the risk by ensuring the third party is trustworthy (legitimate businesses do not generally spend their time messing with people's itineraries) and by redacting information unnecessary to their purpose (if they're picking you up at the airport, they may need the information of your arrival flight but not the booking code). Or you may conclude that the third party is trustworthy and necessary and provide the information.
Instead of subtracting sensitive information, it may be more straightforward to start with nothing and add non-sensitive information. In general, if you provide the (departure) date, airline, and flight number, that should be enough for anyone to look up the time, duration, both airports, gate, and terminal, as well as check for delays (e.g. by putting the airline and flight number into Google). Some flights consist of multiple segments, so you may also need to indicate which segment you're talking about. Depending on your situation, you might also want to tell them your name, seat assignment, cabin class, or any other personal information which they legitimately need to know.
In general, there is no good reason to provide anyone with your booking code or confirmation number (or whatever your airline calls it). The only purpose of this code is to check-in, rebook, cancel, or otherwise mess with your flight, and nobody besides you should be doing any of those things. If anyone asks you for this code, you should refuse to give it to them unless they are affiliated with the airline or your travel/booking agency.
