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If a player gets injured in a match, there are substitutes to replace.
What about umpires?
I saw a news in BBC site dated 5 July 2009 that,
An old umpire of aged 72 got died after being hit on the head by a ball. That match got abandoned and it was only a domestic league match.
What is the rule for this in international matches that an umpire got injured?
There is always a reserved umpire in any match. So if any umpire get injured the reserved umpire is called for umpiring. Mostly host nation's umpires are used as reserved umpires. See in a Test match between New Zealand and West Indies Gregory Brathwaite is a reserved umpire.
If an onfield umpire is ill or injured in an international match, then he is replaced by the third umpire. The duties of the third umpire are then performed by the fourth umpire.
An example of this was 1st ODI: India v Australia at Vadodara where the planned umpire Mark Benson fell ill shortly before the match, and was replaced by the planned 3rd Umpire, Amish Saheba.
As a side note: the link you gave was to the unfortunate case of the umpire dying on the pitch. Here, extra considerations to the feelings of players, coaches, officials and the public would have to be made. I assume the match was abandoned for these reasons, and that it would almost always be possible to find a suitable replacement to act as a square-leg umpire for a local match.
Certainly at the local level here in the uk for non serious injury we would use a player or spectator as the square leg or non strikers end umpire whilst standing at the bowlers end for both bowlers.
At representative and first class level you will have a reserve / 3rd umpire appointed who would take over the duties of the umpire who had become incapacitated.
At international level there is always a 4th umpire as well as the tv umpire who can undertake provide cover for the on field umpires.
The Fourth Umpire/Reserve Umpire is on stand-by in case the on-field umpires or the third umpire are not in a position to perform their duties due to various reasons.