This is largely taken from a post I wrote about this topic some months ago. The long and the short of it is that while the exact location is no longer known, people are still willing to look.

Alexander was supposedly originally entombed in Memphis and later moved to Alexandria by either Ptolemy I or Ptolemy II and was probably moved again later on by Ptolemy IV. This last known resting place was said to be found at the crossroads between the north-south and east-west arteries of the city. Just what happened to it remains unclear.

The latest mention of the body of Alexander comes from 215 under the emperor Caracalla. According to contemporary historians Cassius Dio and Herodian, Caracalla was obsessed with Alexander and had a strong desire to emulate the great conqueror. Herodian reports that Caracalla went to the tomb in Alexandria, opened up the sarcophagus, and placed his purple cloak and other assorted valuables inside. He then went back to his regularly scheduled business of massacring the Alexandrians because they weren't treating him with the respect he felt he deserved.

That is the last historical record of someone visiting the body of Alexander. What happened to it afterwards is a mystery. It is possible that the site was destroyed during Aurelian's campaign of 273 or that simple coastal erosion has consigned the tomb to the waves. However, mentions of a site alleged to be Alexander's tomb feature in later reports of Arab writers Ibn Abdel Hakam (A.D. 871), Al-Massoudi (A.D. 944), and Leo the African (sixteenth century). As mentioned in a piece on the subject in a publication for the Archaeological Institute of America, all these accounts mention such a place but do not give its exact location.

Despite the mystery that pervades this subject, there has been no shortage of effort expended on finding the tomb of Alexander. The medieval accounts mentioned above may well reference the real tomb and plenty of people have spent a lot of time and money trying to find it. Some 140 officially recognized attempts to find the site have been mounted over the years but with no success. A popular local legend states that the tomb lies below or near the Nebi Daniel mosque but it's not clear what evidence, if any, this supposition relies on. It may well be little more than nineteenth century romanticism. A team of Polish researchers working in the 1960s determined that the network of tunnels underneath the mosque were ancient cisterns rather than any kind of tomb. People still believe the legend though and subsequent, but fruitless, excavations have since taken place at the mosque. Other researchers of lesser repute have posited various alternative theories about the tomb's location but with little solid evidence.

The sum total of all this is that we don't really know what happened to Alexander's sarcophagus and tomb after the visit of Caracalla in 215. Coastal erosion may well have swallowed up the site but the fact that the location is so uncertain leaves us without a definitive answer. It may have been destroyed by Aurelian's war in 273 but we cannot say for sure. It is plausible that some or all of the later accounts refer to the real tomb and that it was still around by as late as the 16th century but specific details are lacking. Lots of people have looked for it without success but this is no deterrent for the most determined. No one has found any record of Alexander's earlier resting places either. In any case, Alexander's body has been an item of intense interest to a lot of people for over 2300 years (a war was fought over its custody after all) and this interest shows no sign of letting up.

For more see the article referenced above and The Quest for the Tomb of Alexander the Great by Andrew Chugg.

Alexander's tomb was a magnificent building in Alexandria or as it was known the Soma. So, considering the building must had been lavishly decorated then it probably most of it's marbles and other important objects were stolen either during Caracalla's sacking of the city; Aurelian's sack of the city in 273 or Diocletian's sack in 297. So with alll the destruction the city suffered during the III century the tomb must have suffered an equal damage, the earthquake the city suffered in 365 must have destroyed most of the tomb, maybe that's the explanation why people at V century didn't know where his tomb was or even who he was. Perhaps the Theodossious edict that outlawed paganism had a consequence in the tomb, if we look how christians destroyed the Serapeum, perhaps Alexander's tomb had a similar fate. But that's not the only question, although the tomb might had been destroyed either by war or earthquakes, the mummy could still be found. There's a theory that St. Mark's body in Venice is not really him but instead Alexander. According to pagan historians, his body was burnt by pagans, so when in the IV century venetian merchants stole the body from Alexandria they actually were carrying Alexander's mummy. But until the priests who guard the mummy approve a carbon dating of the body we will never known if that mummy is indeed Alexander.