Cloud services must be continuously monitored to guarantee that misbehaviors can be timely revealed, compensated, and fixed. While simple applications can be easily monitored and controlled, monitoring non-trivial cloud systems with dynamic behavior requires the operators to be able to rapidly adapt the set of collected indicators. Although the currently available monitoring frameworks are equipped with a rich set of probes to virtually collect any indicator, they do not provide the automation capabilities required to quickly and easily change (i.e., deploy and undeploy) the probes used to monitor a target system. Indeed, changing the collected indicators beyond standard platform-level indicators can be an error-prone and expensive process, which often requires manual intervention. This paper presents a Monitoring-as-a-Service framework that provides the capability to automatically deploy and undeploy arbitrary probes based on a user-provided set of indicators to be collected. The life-cycle of the probes is fully governed by the framework, including the detection and resolution of the erroneous states at deployment time. The framework can be used jointly with existing monitoring technologies, without requiring the adoption of a specific probing technology. We experimented our framework with cloud systems based on containers and virtual machines, obtaining evidence of the efficiency and effectiveness of the proposed solution.