The border closure is the latest escalation in a diplomatic crisis that has broken out between Rwanda and DR Congo.
The Democratic Republic of Congo closed its border with Rwanda hours earlier after a Congolese soldier was shot dead while attacking border guards inside Rwandan territory.
The border closure is the latest escalation in a diplomatic crisis that has broken out between the two neighbours since rebels that DRC accuses Rwanda of supporting launched a major offensive in eastern Congo last month.
Rwanda denies Congo's allegations that it supports the M23 rebels, whose leadership hails from the Tutsi ethnic group, or that it has sent troops into eastern Congo.
Congo's government ordered the border with Rwanda closed on Friday as of 3 pm local time (1300 GMT) instead of the daily closing time of 10 pm, according to a statement from the office of South Kivu's governor.
Two Rwandan police officers were injured when the Congolese soldier crossed the border and opened fire, before an officer on duty fired back and killed him 25 metres inside Rwanda, the Rwandan military said in a statement.
Congo's government said it was investigating the incident.
*Story updated to reflect that the DRC government ordered the border closed earlier than its usual time of 10pm following the shooting incident.