His trainer Abdullah bin Huzaim has also been banned for a year.
Sheikh Mohammed, who is married to FEI president Princess Haya, rode Tahhan in a CEI 2* 120km in Sakhir, Bahrain on 10 January and in a CEI 2* 120km in Dubai on 28 February.
Samples taken on both occasions proved positive for a hypertension drug, Guanabenz, and on one for the steroid 16-b Hydroxy-Stanozolol.
The sheikh, who rides for the United Arab Emirates (UAE) did not ask for a second, or “B”, test to be made on either samples.
In his submission to the disciplinary committee the sheik said he has an interest in some 700 endurance horses and cannot be involved in the medication protocol of each.
He was presented with the horse on both occasions only minutes before the race started and had been assured everything was in order.
In a statement his trainer Abdullah bin Huzaim admitted administering the drugs to the horse without the sheikh’s knowledge.
But under FEI rules the rider is always responsible for drugs infringements and the tribunal issued a statement saying “it is the responsibility of competitors to inform themselves of all substances administered to [their] horses”.
The trainer was also found to be responsible for the breach.
The FEI tribunal issued its decision on 31 July and said it took into account how the sheikh effectively banned himself from competition in April, before he was aware of the FEI investigation, after his own tests on the horse showed drug traces.
The sheikh’s ban runs for six months until 3 October and he was fined CHF 3,000 (£1,666) with CHF1,500 (£833) costs.
On 22 July another UAE endurance rider, Sultan Ahmed bin Sulayem, was suspended from competition for six months and his horse, Bebabeloula, for 12 months.
The horse tested positive for the painkiller Butorphanol and sedative Hydroxyxylazine at a CEI 3* 120km at Al Wathba in the UAE on 13 December 2008.