Racial hate crimes - the most common form of hate crime in Scotland - also increased slightly in 2013-14, official statistics showed.
There were 4,148 such charges brought against people last year, accounting for almost 69% of all hate-crime charges.
While there was a 3% rise in racial crimes last year, the total for 2013-14 was also the second lowest since reports began.
A total of 890 crimes against people because of their sexuality were reported last year - a rise of 22% on 2012-13 - making it the second most common form of hate crime.
Meanwhile, a 12% increase in hate crimes against disabled people saw 154 such offences reported last year.
Scotland's top prosecutor, Lord Advocate Frank Mulholland QC, said he was concerned by the rise in offences linked to race and sexual orientation.
"Offending motivated by racial prejudice is at its second lowest level since 2003-4 despite a 3% rise," he said.
"However, there are still too many incidents in which people are targeted because of their race and we are firmly committed to prosecuting such crimes.
"I recently called on those affected by crime motivated by disability to come forward and report it to the police.
"I have long suspected these crimes are under-reported and I hope the 12% rise in reported crimes in this area is a result of the work prosecutors and police have done to gain the trust of this community.
"However, I am concerned about the increases in offences motivated by prejudice against sexual orientation and race.
"These show that there is still work to be done in those areas. I have said it before and I will say it again, there is no place in a modern Scotland for any behaviour motivated by prejudice and it will not be tolerated.
"We are heading in the right direction and I am confident that in time such offences will reduce as Scotland becomes an even fairer and more tolerant society to live in."
Offences with a religious aggravation, including those prosecuted under legislation aimed at curbing sectarianism in football, fell by 17% to 635 - the lowest total since 2009-10.
The Offensive Behaviour at Football and Threatening Communications Act came into force in March 2012, with 203 charges brought under this of religiously aggravated crimes in and around football matches in 2013-14, a drop of 24% on the previous year.
Last year also saw 25 charges of hate crimes against transgender people, up from 14 in 2012-23.
Mr Mulholland said: "The figures published today show we are making progress in tackling some aspects of hate crime in Scotland.
"However, it is also clear that more needs to be done in other areas and we remain resolutely committed to doing so."
He said the 24% drop in charges of religious offences in and around football matches was "encouraging" and added: "The statistics show that over the last year there has been an average of one criminal charge for every five regulated football matches which have taken place in Scotland.
"While the Act has only been in force for two full years and therefore is too soon to conclude this is a trend, football grounds have in general been a safer, more tolerant environment over the last couple of years.
"It is also reassuring to see a reduction of around 15% in criminality motivated by religious prejudice, which is now at the lowest level for nine years."
Equalities Secretary Shona Robison said: "No-one should have to face discrimination or prejudice in any form in 21st-century Scotland. It is never acceptable and it will not be tolerated.
"That's why we have been working closely with organisations and police to eradicate hate crime from Scottish society."
She said more than £60 million was being spent on tackling inequality and discrimination between 2012 and 2015 which "shows that we take this issue very seriously".
Ms Robison added: "The more we talk about it, the easier it will be for people to report hate crimes to the authorities.
"We are not becoming more intolerant as a society but we are becoming less tolerant of those who hold prejudiced beliefs."