Besides Chief Minister Arvind Kejriwal, who does not hold any portfolio, the city government is presently functioning with four ministers.
Mishra was sacked on May 6 and two AAP legislators - Rajendra Pal Gautam and Kailash Gehlot- were inducted.
A top official in the government said the files pertaining to the appointment of Gautam and Gehlot were sent to the Home Ministry just after the city Cabinet decision to remove Mishra.
According to the official, works in the sectors like water, tourism, social welfare and women and child welfare are getting affected as these departments are "headless" for quite some times.
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Mishra had the portfolio of water, tourism, art and culture.
AAP MLA Sandeep Kumar was sacked from the Delhi Cabinet after a sex video allegedly involving him emerged last August.
No new face had replaced Kumar and Deputy Chief Minister Manish Sisodia has been taking care of his portfolios - social welfare, women and child welfare and others.