Do I have to pay taxes on profits earned from mutual fund investments?

Yes you will have to pay taxes on the gains that you’ve earned after withdrawing your mutual funds. These taxes are applicable on the type of funds and Gain type.

Fund type     
Stocks of domestic companies
Equity funds including Tax saving funds and equity-oriented funds     
Minimum 65% investment
Hybrid funds Between 35% and 65% investment
Debt funds including liquid funds and international equity funds Less than 35% investment

Tax applicable for equity funds including tax saving funds and equity-oriented funds with minimum 65% investment in equity shares of domestic companies.

Note: Some balanced advantage funds in equity funds have more than 65% of domestic stocks fall under indexation benefits and are termed as equity-oriented funds.

Type of Fund Gain Type Short Term Capital Gain Long Term Capital Gain
Equity- oriented funds Duration Investments sold within 1 year Investments sold after 1 year
  Tax Rate Your gains will be taxed at the rate of 15% (plus applicable surcharge and cess) Gains will be taxed at the rate of 10%(plus applicable surcharge and cess) if the capital gains exceed Rs 1 lakh a year. 
Hybrid funds Duration Investments withdrawn within 3 years. Investments withdrawn after 3 years.
  Tax Rate Taxed at marginal rate depending on your income slab (plus applicable surcharge and cess) Taxed at 20% after indexation (plus applicable surcharge and cess).
Debt Funds Duration These investments can be withdrawn throughout the year. NA
  Tax Rate Taxed at a marginal rate depending on your income slab (plus applicable surcharge and cess). NA

Important Points:

Please consult a tax consultant or advisor for more information.

Related question(s):
Are mutual funds regulated?
What is indexation and what are its benefits?