The legislator with tight police security left his house in Banjara Hills for Gandhi Hospital at 10.30 a.m. after a team of police officials from Nirmal town of Adilabad district served a notice, asking him to undergo the medical tests.
A senior police official said after the medical tests, they would decide their next legal action in the case.
MIM leaders including party chief and Member of Parliament Asaduddin Owaisi were at Akbar's house before he left for the hospital.
A large number of MIM workers had also reached there.
Akbar, who returned from London early Monday, sought four days' time to appear before police, citing ill-health.
He was directed by the police to appear in Nirmal town police station, about 200 km from here, for questioning with regard to his alleged hate speech delivered last month.
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Investigating officer had Monday night visited Akbar's house.
Inspector General of Police A.B. Venkateshwar Rao later told reporters that the investigating officer found Akbar in a fit condition but the legislator complained of some "internal pains".
Police in Nizamabad had also directed Akbar to appear before them Tuesday in connection with a similar case in that town.
The young leader, however, through his lawyer sought more time to make personal appearance.
Akbar, who is MIM member in the Andhra Pradesh assembly, also moved the state high court, seeking orders to restrain police from arresting him.
He also pleaded that the police be directed not to book further cases. The petition is likely to come up for hearing Wednesday.