What we can say may depend on some specific aspects of the experiment considered.
If you consider just one closed physical system then we can say yes, physically, the observation of its state requires to physically interact with it, and thus affect it.
For example if you have one electron and want to measure its spin in the up/down direction, you must interact with it so that if its spin was previously rightwards (which means : a 100% probability of finding it so if you measure it in the left-right direction), then the required interaction for the up/down measurement process has the physical effect of destroying the left/right component of the spin, and thus leading to equal chances for it to be found leftwards or rightwards if you measure it in the left-right direction after this.
This is also the case in the double-slit experiment : the observation of which slit a particle goes through, requires some sort of physical interaction with this particle when it goes through.
Such an explanation may turn out to be unsatisfactory when we consider some experiments where the effect on the probability of final result is greater than what seems to be the "probability of physically affecting the system", for example in the case when one slit is bigger than the other and you detect the particle going through the small slit.
Other cases may be ambiguous : in the EPR experiment, or in the Schrodinger's cat experiment when an observer would receive at distance the information on what happened to the cat (in the theoretical view that the cat did not already observe itself), observing one particle somehow "affects" the other at distance, but the relevance of the words is not clear, whether or not we can really say that measuring the one "affects" the other.
For this, it may be necessary to enter the effective mathematical expression of what quantum physics says, how it describes measurements, and how ambiguous it is on the interpretation. See my introduction to quantum physics (settheory.net/quantum-measurement ) for detailed explanations of how measurements are processed and how they "affect" systems.
