The Jamia Masjid Abu Huraira - also known as Beeston Central Mosque - on Hardy Street and the Guru Nanak Nishkam Sewak Jatha, a Sikh gurdwara on Lady Pit Lane were set on fire just before 4am on Tuesday morning.
A flammable liquid was used to ignite both front doors but fire crews managed to contain the blaze before it spread.
Pritpal Singh, from Leeds, took to Twitter to share his anger.
He said: “Gutted to hear my local Gurdwara in Leeds was attacked in the early hours in a suspected racist attack.
"Have spoken to them on the phone and spirits are high but there is anger that it has come to this.
"The local mosque was also attacked at the same time.
"The GNNSJ Gurdwara in Leeds is a real outward-facing pillar of the south Leeds community.
"You can regularly go there and see people of all faiths and races partaking in langar. Awful that it has been targeted in this way."
John Vowles said on the Yorkshire Evening Post's Facebook page: “It's idiots who do stuff like this to create divide - it also fuels reprisal attacks.
We should stand together against hatred racism and any other scum of the earth what tries to derail are multicultural society”
Mandi P Bayston said: “Hope who ever has done this realises the trouble it can cause...I personally think it was a hate crime and it's got to stop.
"We all live here, we are not going anywhere soon so why can't we all just get on we get good and bad in all walks of life but targeting mosques is just adding fuel to the fire (excuse the pun). Shame we can't all live together in bloody peace.”
Sophie Louise said: “Hope everyone is safe and that they manage to out the culprits away for a very long time.”
Craig Farquharson said: “Disgusting what's wrong with some people. Lack of education.”
Rick Poppa said: Why can't everyone, no matter what faith you are just get along! There is just no need for things like this to happen!
Andrea Allan said: “I'm not particularly a follower of any religion, but I do respect the fact that others do. I still appreciate architecture of buildings such as churches mosques, synagogue, sikh temples etc noone has any right to damage such places. Idiot!“
Philip Millard said: “Some people have no brains so disrespectful hopefully whoever did this is caught and brought to justice.”
Police believe the crimes are linked.
Detective Inspector Richard Holmes, of Leeds District CID, said: “While our investigation is still at a relatively early stage, we do believe these premises have been specifically targeted as places of worship and we are treating both incidents as arson and hate crimes.
“We are currently carrying out extensive enquiries, including checks on CCTV in both areas, and we would like to hear from anyone who has witnessed any suspicious activity or seen any person or vehicles in the areas around the time these incidents have occurred.
“We would also like to hear from anyone who has any other information that could assist the investigation.
“Clearly we will always treat incidents of this nature very seriously and will be doing everything we can to identify those responsible and bring them to justice.”
Inspector Ian O’Brien, who heads neighbourhood policing for south Leeds, said: “These incidents will cause an understandable level of concern in both the Muslim and Sikh communities in this area and we are working closely with key representatives from those communities to reassure them.
“We have increased our patrols of the area to provide visible reassurance to people living there and will continue to keep key community representatives informed as the investigation develops.
"Hate crimes that target particular communities and have the potential to cause divisions and tensions cannot and will not be tolerated and we will continue to do everything we can to find those responsible and support and reassure the communities affected.”