No, a fixed deposit does not count towards the minimum balance.
I do have to appreciate you, if you come to this article searching such a logical question.
The minimum balance requirement is for Saving Accounts (and Current Accounts), it is not waived if you do any other business dealings with the bank.
Technically, a fixed deposit is another form of account, and it is a separate entity. As you promise to keep a certain sum for a fixed period of time with the bank, and in return the bank gives you a higher interest rate.
In a saving account there is no such agreement between you and the bank. You can keep as little and as much money as you like and take it out and deposit it as and when you like. But to make the account feasible and self digest its basic charges like debit card fees, the clause of minimum balance has been introduced.
The bank takes in deposits and in return provide interest as an incentive to you to deposit your ideal cash. This money, that you deposited with the bank, is provided as a loan to other people who are in need of loans.
The banks, in this case, charge money for the service they provide.
This is the basis of banking. When you open a saving account with a bank, the bank imposes a minimum balance clause to ensure that the dealing is at the very least fair to the bank and that how a bank maintains feasibility.