One blast occurred in the busy Mwembe Tayari area of the city centre, and the other close to a well-known beach hotel, the Reef Hotel, in the Nyali area of the city.
The Kenyan interior ministry said three people were killed and around 15 wounded in Mwembe Tayari after one or more grenades were thrown into a crowded passenger bus that had just arrived from the capital Nairobi.
The ministry also said an improvised explosive device, or IED, went off at the gate of the Reef Hotel, although no casualties were reported. The hotel's management said all its staff and guests were safe.
There was no immediate claim of responsibility, although the city has been on high alert for possible attacks by Somalia's Shebab rebels or local Islamist militants.
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Muslim-majority Mombasa, a port city that is one of the main gateways to east Africa as well as a popular tourist destination, has been hit by sporadic unrest in recent months.
The city has been rocked by a string of attacks or attempted attacks, with security forces engaged in a major and controversial crackdown against Islamists suspected of being connected to neighbouring Somalia's Al-Qaeda-linked Shebab rebels.
The Islamist group claimed responsibility for the high-profile attack on Nairobi's Westgate shopping mall last year in which at least 67 people were killed.
In March two people were arrested in Mombasa along with a car expertly packed with explosives. Intelligence sources say they believe the car was rigged in Somalia and driven into Kenya for a high-profile bombing.
Also in March, six worshippers were shot dead in a church in Likoni near Mombasa.
The cleric, Abubaker Shariff Ahmed better known as Makaburi, was a vocal supporter of Al-Qaeda and the Shebab and was on a UN sanctions list for allegedly recruiting militants.