Stoltenberg pledged a "measured, defensive" response if Russia did not come back into compliance with the deal by the August 2 deadline.
"We have to be prepared for a world... with more Russian missiles," he told the BBC.
The 1987 agreement signed by the US and USSR banned short and medium-range missiles.
US President Trump announced the US would suspend its obligations under the Intermediate-Range Nuclear Forces (INF) Treaty in February, accusing Russia of breaching its terms.
Russia denied the allegation but suspended its own obligations shortly afterwards and announced plans to develop new weapons systems.
In an interview with the BBC, Stoltenberg said the Russian missiles - which he says are in "clear violation of the treaty" - are nuclear capable, mobile, very hard to detect, and able to reach European cities within a few minutes.
"This is serious. The INF treaty has been a corner stone in arms control for decades and now we see the demise of the treaty," he said.
While the priority was to get Russia to come back into compliance with its terms, Stoltenberg said there were "no signs whatsoever" the country will do so. Therefore, we have to be prepared for a world without the INF treaty and with more Russian missiles."
While Nato has no plan to deploy nuclear land-based missiles of its own in Europe, Stoltenberg said the alliance would respond in a "measured, defensive way" if Russia refused to come back into compliance by August 2.
Conventional air and missile defence, new exercises and readiness of forces, and new arms control initiatives could all form part of that response, he said. Any final decision will come after the deadline.
Stoltenberg also addressed Russia's delivery of its advanced S-400 missile defence system to Nato member Turkey last week.
The US says it will remove Turkey from its F-35 fighter jet programme in response. Ankara has recently moved closer to Moscow, raising tensions between Turkey and the US.
"It is a serious issue because it is a serious disagreement which involves two important allies," Stoltenberg said. Nato supports efforts to resolve the disagreement, he added, while praising Turkey's key role in the organisation.
( With inputs from IANS )