HTTP-Proxy-Servlet does exactly what you need.
Quick configuration
pom.xml
<dependency>
    <groupId>org.mitre.dsmiley.httpproxy</groupId>
    <artifactId>smiley-http-proxy-servlet</artifactId>
    <version>1.7</version>
</dependency>
web.xml
<servlet>
    <servlet-name>solr</servlet-name>
    <servlet-class>org.mitre.dsmiley.httpproxy.ProxyServlet</servlet-class>
    <init-param>
        <param-name>targetUri</param-name>
        <param-value>http://solrserver:8983/solr</param-value>
    </init-param>
    <init-param>
        <param-name>log</param-name>
        <param-value>true</param-value>
    </init-param>
</servlet>
<servlet-mapping>
    <servlet-name>solr</servlet-name>
    <url-pattern>/solr/*</url-pattern>
</servlet-mapping>
Spring Integration
see also: HTTP-Proxy-Servlet Issue #15
pom.xml
<dependency>
    <groupId>org.mitre.dsmiley.httpproxy</groupId>
    <artifactId>smiley-http-proxy-servlet</artifactId>
    <version>1.7</version>
</dependency>
ServletWrappingControllerExt.java
import javax.servlet.http.HttpServletRequest;
import javax.servlet.http.HttpServletRequestWrapper;
import javax.servlet.http.HttpServletResponse;
import org.springframework.web.servlet.ModelAndView;
import org.springframework.web.servlet.mvc.ServletWrappingController;
public class ServletWrappingControllerExt extends ServletWrappingController
{
    private String  pathToStrip;
    public void setPathToStrip(String pathToStrip)
    {
        this.pathToStrip = pathToStrip;
    }
    @Override
    protected ModelAndView handleRequestInternal(HttpServletRequest request, HttpServletResponse response)
            throws Exception
    {
        final HttpServletRequest wrapper = new HttpServletRequestWrapper(request)
        {
            @Override
            public String getPathInfo()
            {
                //Please note that getPathInfo returns null if DispatcherServlet is configured to track url-pattern "/"
                //It should be configured to track url-pattern "/*". Below is a sample DispatcherServlet configuration
                /*
                    <servlet>
                        <servlet-name>spring</servlet-name>
                        <servlet-class>org.springframework.web.servlet.DispatcherServlet</servlet-class>
                        <load-on-startup>1</load-on-startup>
                    </servlet>
                    <servlet-mapping>
                        <servlet-name>spring</servlet-name>
                        <url-pattern>/*</url-pattern>
                    </servlet-mapping>
                 */
                String path = super.getPathInfo();                  
                if (path.startsWith(pathToStrip))
                {
                    final int length = pathToStrip.length();
                    path = path.substring(length);
                }
                return path;
            }
            
            @Override
            public String getServletPath()
            {
                return super.getServletPath();
            }
        };
        return super.handleRequestInternal(wrapper, response);
    }
}
Beans configuration
<bean id="myServletWrapper" class="ServletWrappingControllerExt">
    <property name="pathToStrip" value="/solr"/>
    <property name="servletClass" value="org.mitre.dsmiley.httpproxy.ProxyServlet" />
    <property name="servletName" value="solr" />
    <property name="initParameters">
        <props>
            <prop key="targetUri">http://solrserver:8983/solr</prop>
            <prop key="log">true</prop>
        </props>
    </property>
</bean>
<bean id="myServletUrlMapping" class="org.springframework.web.servlet.handler.SimpleUrlHandlerMapping">
    <property name="urlMap">
    <map>
        <entry key="/solr/**" value-ref="myServletWrapper" />
    </map>
    </property>
    <property name="order" value="1" />
</bean>