Meetings in Austria and Switzerland have also been banned.
The comments drew a sharp response from German leaders, with Chancellor Angela Merkel describing the comparison as “unacceptable”.
Rotterdam Mayor Ahmed Aboutaleb said the owner of the hall that had been scheduled to hold Mr Cavusoglu’s event in the city on Saturday had withdrawn authorisation, but the foreign minister could still visit.
There was also uncertainty about whether an event he was due to attend in Zurich, Switzerland, on Sunday would go ahead after one venue refused to hold it.
Relations between Turkey and European countries have deteriorated since last July’s attempted coup in Turkey. Germany has been critical of the mass arrests and purges that followed – with nearly 100,000 civil servants removed from their posts and academics among the latest.
Turkey is a key partner in an arrangement attempting to limit the movement of migrants into the EU, but has threatened to “open the gates” if the EU reneges on commitments to provide aid, visa-free travel for its nationals and accelerated membership talks.