I had same issues with dnsmasq and logrotate on ubuntu 20.04. Here is my solution:
In /etc/dnsmasq.conf the following entry is required:
log-facility=/var/log/dnsmasq/dnsmasq.log
Create /etc/logrotate.d/dnsmasq with the following content:
/var/log/dnsmasq/dnsmasq.log { size 100M weekly rotate 7 compress missingok notifempty postrotate service dnsmasq restart endscript }
The important thing was the restart of dnsmasq!