Kenny MacAskill said Police Scotland have launched extensive inquiries into the incidents.
He updated Holyrood the day after thousands of people took part in a midnight march in the south side of the city. Organisers said they were tired of being told they should not go out at night alone.
Recent attacks include a gang assault in Toryglen, the rape of a 24-year-old woman in Govanhill, and an alleged rape in the Merchant City area last weekend.
Mr MacAskill said: "The sexual assaults that have taken place in the Glasgow area, including the incident last Sunday, are very distressing.
"There has been an increase in both the foot patrols and car patrols, not only in the Govanhill area but indeed elsewhere where incidents have taken place."
The Justice Secretary will meet with the charity Rape Crisis Scotland tomorrow.
Labour MSP for Glasgow Anne McTaggart called for assurances that police patrols would be stepped up, raising her concerns over "backfilling" of officers into civilian roles following the creation of the single police force.
Mr MacAskill said: "I think what is important is that we allow the police to get on with doing their job, to apprehend those that have carried out these appalling acts and bring them to justice.
"I am not going to bandy around statistics, who voted for what, or 1,000 extra police officers.
"I think what we are here to do is to give our support to those who are carrying out the investigation.
"The benefit of the Police Scotland is that we do now have a national rape taskforce and major investigation teams in different geographical areas."