I guess for this to happen, we need someone powerful enough to build such a dam, but stupid enough to actually build it...
So, therefore, let's try something different.
POD: about 1000 AD
Al-Andalus survives, and extends its reach. It ends up as a caliphate covering OTL Morocco, Algeria, Spain, Portugal, UK, France, and the Low Countries. By 1500 virtually all of the population is Muslim, and speaks Arabic.
There's a strong Muslim/Christian divide in Europe, though both are progressing technologically at similar rates.
Most Christian Europeans fear the advance of the Muslims. United by a common religion, the Byzantine Empire turns into a theocratic Catholic state, and absorbs many of its former territories to keep the population safe.
For nostalgic reasons, its capital is moved back to Rome. Both Andalusia and the Roman Empire crack down heavily on "heretics", and the theocracies gradually strengthen.
Roman Empire ends up controlling OTL Italy, Greece, the Balkans, Germany, the Baltics, Poland, Ukraine. Scandinavia becomes a neutral-ish Viking empire.
With scientists persecuted by the state, technological development stagnates in Europe, seemingly permanently. The cultures of the empires slowly start to homogenize.
Come 2200 CE. China, and its vicinity, is divided into several rival states, starting to develop technologically. The main states are Hui, Han, Mongolia, Manchuria, Korea, Japan, and the Ainu state on Hokkaido and Sakhalin.
2200 CE China ITTL is an analog to OTL 1500 CE Europe.
2200 CE Europe ITTL is an analog to OTL 1500 CE China.
America is discovered in 2186 CE by a Japanese trading ship seeking to find a naval trade route to Europe.
Japan has the strongest navy in the world, due to its unique position on the sea. Many nations colonize the Americas, but Japan is most successful.
By 2450 CE, Industrialisation is now well underway in much of East Asia.
Japan and Han, the two main empires, cover much of the globe, spreading new technology to the natives. Other states, such as Korea and Ainu, play a role.
Europe is colonized; the Roman and Andalusian empires finally fall to the conquerors by 2550 CE.
Decolonization comes eventually, but such states still remain with the governing systems of their former masters. (Mostly the Republic, a form of representative government invented in the aftermath of the 2366 Manchu Civil War)
The Republic of Andalusia is finally declared independent from Japan in 2641. The government is still corrupt, though, and heavily influenced by religion.
Using their newfound technological prowess, Andalusia begins construction of a dam across the Strait. Such a project takes up a large fraction of the country's budget, but it's seen as being necessary in order to "make more land for our crowded population".
In reality, it's just flipping the bird at Italy. Removal of the sea will cause widespread desertification in the lands of the Christian enemies to the east.
Shame they can't do anything about it. It works, too: Italy became little more than searing desert after the dam was formed. But the dam is very well defended by Andalusia.
Eventually, due to concerns of global sea level rise, Korea (controller of the OTL Suez Canal area) digs a canal to allow water to flow back into the Med.
Thus ended the "Seven Years of Hell". It is an event that never should have happened, and will hopefully never happen again.