Well, I can think of one major unintended consequence, just due to the date. If it's an earthquake big enough to cause a natural strait to occur, then I bet it causes some environmental damage to the Red Sea and to the Med. What I'm particularly thinking of is this: 608 AD is less than 20 years before Mohammed is said to have his first revelation and then led the Hijra. A tsunami in the right place could well do a lot to stop that. There will no doubt be other similar effects of the initial POD that will momentarily overshadow the strategic ramifications.
Putting those aside, there is likely to be big change in the ease of transport to Asia. However, it will take some time to come to prominence. For one, naval technology is still based either around galleys or limited ocean-going navigation. Even Phoenician ships seem to stuck fairly close to land and certainly common practice did. It was the harsher climate of the North Sea and Atlantic that encouraged the development of the forerunners of galleons and caracks, that enabled truly transoceanic navigation. Nonethless, there's a lot of land to stop near on this new route; the obstacle is that not only would you need navigable access, you'd also need friendly ports along the way. It's a big distance to cover. Plus, the Red Sea is fraught with navigational hazarads (reefs and the like). This may provide a different incentive to build more sturdy, long range craft, which will definitely shift the nature of TTL's naval tech. To take full advantage of the sea route to India and East Asia, naval tech would need to be advanced enough to take advantage of the monsoon winds. Very probably OTL tech could handle this: if anything it may ease the transistion, since the reliable winds will make it eaiser to a craft to stop for shelter and supplies more regularly. The difference in technological development may also shift the nature of the decline in learning that was already going on in the West: math is all of sudden more important to master for reliable navigation as is map-making and the like.
Geo-politically, it will be harder for a conqueror to surmount this breach, so Egypt may find itself a new power center. Perhaps as part of the Eastern Roman Empire, perhaps as an empire all its own. A new city along the new Suez Straights may develop as a rival to Constantinople.
On the flip side, though, what's the incentive to trade? It's so early in history that there might not be enough of a market at home to incentive a trader. There probably is enough of one, though, in the Eastern Empire. Certainly, Mohammed was a trader before he turned to religion. Perhaps the upsurge in trade changes the nature of Arab culture. Since this change will empower Red Sea traders to expand into the Mediterranean, this change could well be credited with transforming Arab culture. What religion would they adopt? Some form of Christianity? Would a new faith emerge in an even more afluent society, with a better escape valve for the less previliged (assuming less powerful traders could risk the new passage to new trade routes and hence new wealth).