First Minister Nicola Sturgeon has urged people not to allow terrorism to triumph after the Manchester bombing.
She was speaking after a late night meeting of the Scottish government’s resilience committee, which discussed security at public events.
Scottish teenager Eilidh MacLeod remains missing while her friend Laura MacIntyre suffered serious injuries.
Six people were also treated at Scottish hospitals after returning from Manchester following the attack.
Four of those patients have since been discharged. Two remain in care, but their injuries are not life threatening.
Monday night’s attack at the Ariana Grande concert at the Manchester Arena left 22 people dead and 59 injured.
The Scottish government’s resilience committee met for a third time late on Tuesday after the UK’s security level was raised to “critical”, its highest alert status.
Ministers were briefed by Police Scotland about the practical implications for Scotland for coming major events such the Scottish Cup Final.
In a statement afterwards the first minister said: “While raising the UK terror threat level to ‘critical’ has been judged a necessary response to the despicable attack in Manchester, we must not allow terrorism to triumph.
“I urge the people of Scotland to be vigilant but not alarmed and, as far as possible, to go about their business as usual.
“Police Scotland have already visibly increased their presence in locations such as transport hubs and city centres as a precaution.
“Security arrangements for upcoming public events, including this weekend’s Scottish Cup Final, are being thoroughly reviewed and the public should anticipate additional safety measures such as full body and bag searches.
“Our emergency services prepare extensively for situations such as this, and those well-rehearsed plans are now being put into practice.”
She added: “Anyone who was in Manchester and witnessed the terror attack or its immediate aftermath will undoubtedly be feeling stressed or upset.
“Anyone with concerns about themselves or their children should contact their GP for support or NHS 24 if their GP surgery is closed.”
Scotland’s Justice Secretary Michael Matheson told BBC Radio’s Good Morning Scotland programme that preparations had been put in place overnight to ensure “the right level of security was in place”.
He said: “Police Scotland have significantly increased the number of armed officers on duty.
“There’s been an increase in the number of armed response vehicles and officers at key locations, such as our main transport hubs and other large infrastructure areas where people gather.”
Political campaigning in the general election has also been suspended for a second day with no events planned in Scotland on Wednesday.
Police have named the suspected suicide bomber as 22-year-old Salman Abedi, who died in the blast after detonating an improvised explosive device he had been carrying, at about 22:35 on Monday night.
So-called Islamic State has said it was behind the attack, via IS channels on the messaging app Telegram.
Anyone who has concerns about loved ones should contact the Greater Manchester Police emergency number on 0161 856 9400.
Analysis: Gordon Corera, BBC security correspondent
The UK threat level has been has been judged to be severe for nearly three years – which means an attack is considered highly likely.
But in recent months the tempo of counter terrorist activity has been increasing with – on average – an arrest every day.
After the attack in Westminster by Khalid Masood in March, police and security officials have been warning that further attacks were almost inevitable.
But they also believed that those were more likely to be low-tech involving knives or vehicles. The fact that the Manchester attack involved explosives will worry them.
It may not have been at the level of complexity seen in Paris in 2015, when multiple attackers sent from Syria used guns and suicide belts, but it will still have required planning to make an improvised explosive device.